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#analyst-notes #cfa-level-1 #corporate-finance #introduction #reading-35-capital-budgeting
Question
Projects concerning expansion into new products, or markets involve [...] and explicit forecasts of future demand, and thus require detailed analysis.
Answer
strategic decisions
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Parent (intermediate) annotation
Open itsts also need to compare revenue/cost/depreciation before and after the replacement to identify changes in these elements.
Expansion projects. Projects concerning expansion into new products, services, or markets involve <span>strategic decisions and explicit forecasts of future demand, and thus require detailed analysis. These projects are more complex than replacement projects.
Regulatory, safety and environmenOriginal toplevel document
Subject 1. Capital Budgeting: Introductionood capital budgeting decisions can be made). Otherwise, you will have the GIGO (garbage in, garbage out) problem. Improve operations, thus making capital decisions well-implemented.
<span>Project classifications:
Replacement projects. There are two types of replacement decisions:
Replacement decisions to maintain a business. The issue is twofold: should the existing operations be continued? If yes, should the same processes continue to be used? Maintenance decisions are usually made without detailed analysis. Replacement decisions to reduce costs. Cost reduction projects determine whether to replace serviceable but obsolete equipment. These decisions are discretionary and a detailed analysis is usually required.
The cash flows from the old asset must be considered in replacement decisions. Specifically, in a replacement project, the cash flows from selling old assets should be used to offset the initial investment outlay. Analysts also need to compare revenue/cost/depreciation before and after the replacement to identify changes in these elements.
Expansion projects. Projects concerning expansion into new products, services, or markets involve strategic decisions and explicit forecasts of future demand, and thus require detailed analysis. These projects are more complex than replacement projects.
Regulatory, safety and environmental projects. These projects are mandatory investments, and are often non-revenue-producing.
Others. Some projects need special considerations beyond traditional capital budgeting analysis (for example, a very risky research project in which cash flows cannot be reliably forecast).
LOS
a. describe the capital budgeting process and distinguish among the various categories of capital projects;
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Tags
#cfa-level-1 #corporate-finance #reading-36-cost-of-capital #study-session-11
Question
A company grows by making [...] that are expected to increase [...]
Answer
investments
revenues and profits
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Open itA company grows by making investments that are expected to increase revenues and profitsOriginal toplevel document
1. INTRODUCTION
A company grows by making investments that are expected to increase revenues and profits. The company acquires the capital or funds necessary to make such investments by borrowing or using funds from owners. By applying this capital to investments with long-term benefits, t
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#cfa-level-1 #corporate-finance #reading-35-capital-budgeting #study-session-10
Question
An [...] environment assumes that the company can raise the funds it wants for all profitable projects simply by paying the required rate of return.
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Open itAn unlimited funds environment assumes that the company can raise the funds it wants for all profitable projects simply by paying the required rate of return.Original toplevel document
3. BASIC PRINCIPLES OF CAPITAL BUDGETINGthe first project or new economic conditions are favorable. If the results of the first project or new economic conditions are not favorable, you do not invest in the second project.
Unlimited funds versus capital rationing —<span>An unlimited funds environment assumes that the company can raise the funds it wants for all profitable projects simply by paying the required rate of return. Capital rationing exists when the company has a fixed amount of funds to invest. If the company has more profitable projects than it has funds for, it must allocate the funds to achieve
Tags
#3-1-profit-maximization #cfa-level-1 #economics #microeconomics #reading-15-demand-and-supply-analysis-the-firm #section-3-analysis-of-revenue-costs-and-profit #study-session-4
Question
Overall, the functions of profit are as follows:
Answer
Allocates resources
input factors flow from sectors with economic losses to sectors with economic profit, where profit reflects goods most desired by society.
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Parent (intermediate) annotation
Open itOverall, the functions of profit are as follows:
Rewards entrepreneurs for risk taking when pursuing business ventures to satisfy consumer demand.
Allocates resources to their most-efficient use; input factors flow from sectors with economic losses to sectors with economic profit, where profit reflects goods most desired by society.
SpuOriginal toplevel document
3. ANALYSIS OF REVENUE, COSTS, AND PROFITS Total variable cost divided by quantity; (TVC ÷ Q) Average total cost (ATC) Total cost divided by quantity; (TC ÷ Q) or (AFC + AVC) Marginal cost (MC) Change in total cost divided by change in quantity; (∆TC ÷ ∆Q)
<span>3.1. Profit Maximization
In free markets—and even in regulated market economies—profit maximization tends to promote economic welfare and a higher standard of living, and creates wealth for investors. Profit motivates businesses to use resources efficiently and to concentrate on activities in which they have a competitive advantage. Most economists believe that profit maximization promotes allocational efficiency—that resources flow into their highest valued uses.
Overall, the functions of profit are as follows:
Rewards entrepreneurs for risk taking when pursuing business ventures to satisfy consumer demand.
Allocates resources to their most-efficient use; input factors flow from sectors with economic losses to sectors with economic profit, where profit reflects goods most desired by society.
Spurs innovation and the development of new technology.
Stimulates business investment and economic growth.
There are three approaches to calculate the point of profit maximization. First, given that profit is the difference between total revenue and total costs, maximum profit occurs at the output level where this difference is the greatest. Second, maximum profit can also be calculated by comparing revenue and cost for each individual unit of output that is produced and sold. A business increases profit through greater sales as long as per-unit revenue exceeds per-unit cost on the next unit of output sold. Profit maximization takes place at the point where the last individual output unit breaks even. Beyond this point, total profit decreases because the per-unit cost is higher than the per-unit revenue from successive output units. A third approach compares the revenue generated by each resource unit with the cost of that unit. Profit contribution occurs when the revenue from an input unit exceeds its cost. The point of profit maximization is reached when resource units no longer contribute to profit. All three approaches yield the same profit-maximizing quantity of output. (These approaches will be explained in greater detail later.)
Because profit is the difference between revenue and cost, an understanding of profit maximization requires that we examine both of those components. Revenue comes from the demand for the firm’s products, and cost comes from the acquisition and utilization of the firm’s inputs in the production of those products.
3.1.1. Total, Average, and Marginal Revenue
This section briefly examines demand and revenue in preparation for addressing cost. Unless the firm is a pu
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#conversation-tactics
Question
The singular key to a successful conversation is [...].
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Open itThe singular key to a successful conversation is comfort.Original toplevel document (pdf)
cannot see any pdfs
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#conversation-tactics
Question
Rehearse only your conversational [...]
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Open itChapter 8. Rehearse only your conversational bookends.Original toplevel document (pdf)
cannot see any pdfs
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#percentage-of-completion-method-steps
Question
Step 3 percentage of completion
Answer
Profit=current revenue-Current cost
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Percentage of completion steps to reportiplicas por 100. Ese porcentaje lo multiplicas por el costo estimado
Step 2: Current Revenue: divides el costo acumulado en ese año, lo divides entre el costo estimado total y lo multiplicas por el precio del contrato.
<span>Step 3:Profit=current revenue-Current cost<span><body><html>
Question
NCC = Depreciation + [...] - Cash expenses during the year in which they are capitalized
Answer
non-cash restructuring charges
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Subject 3. Cash Flow Statement Analysis. The tax treatment of all non-cash items is the same as that of other items in the books. There are no differed taxes incurred.
Calculate the FCFF for Proust for the year.
Solution
<span>NCC = Depreciation + non-cash restructuring charges - Cash expenses during the year in which they are capitalized = 130 + 30 - 200 = -$40 million
FCFF = NI + NCC + Int (1 - Tax rate) - FCInv - WCInv = 250 + (-40) + 50 (1 - 0.3) - 20 - 100 = $125 million
FCFF
Question
Net income available to common shareholders is the company's earnings after [...], taxes and [...]
Answer
interest
preferred dividends.
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Subject 3. Cash Flow Statement Analysis;
Free cash flow = CFO - capital expenditure
Free Cash Flow to the Firm (FCFF): Cash available to shareholders and bondholders after taxes, capital investment, and WC investment.
<span>FCFF = NI + NCC + Int (1 - Tax rate) - FCInv - WCInv
NI: Net income available to common shareholders. It is the company's earnings after interest, taxes and preferred dividends. NCC: Net non-cash
Question
Net non-cash charges represent depreciation and [...] minus [...].
Answer
other non-cash charges
non-cash gains
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Subject 3. Cash Flow Statement Analysis;
Free cash flow = CFO - capital expenditure
Free Cash Flow to the Firm (FCFF): Cash available to shareholders and bondholders after taxes, capital investment, and WC investment.
<span>FCFF = NI + NCC + Int (1 - Tax rate) - FCInv - WCInv
NI: Net income available to common shareholders. It is the company's earnings after interest, taxes and preferred dividends. NCC: Net non-cash
Question
What rates are included in the nominal rate of interest?
Answer
real risk-free
inflation.
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Open itThe nominal risk-free rate of return includes both the real risk-free rate of return and the expected rate of inflation. A decrease in expected inflation rate would decrease the nominal risk-free rate of return, but would have no effect on the real risk-free rate of return.
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#discounted-cashflow-applications
Question
What is the NPV Rule rule
Answer
An investment should be undertaken if its NPV is positive but not undertaken if its NPV is negative.
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#reading-8-statistical-concepts-and-market-returns
Question
How much space is there between the bars of a histogram
Answer
There is no space between the bars
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Subject 3. Frequency Distributionsays a frequency distribution. It is constructed as follows:
The class frequencies are shown on the vertical (y) axis (by the heights of bars drawn next to each other). The classes (intervals) are shown on the horizontal (x) axis. <span>There is no space between the bars.
From a histogram, we can see quickly where most of the observations lie. The shapes of histograms will vary, depending on the choice of the size of the interva
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#reading-8-statistical-concepts-and-market-returns
Question
Simply, relative frequency is the [...] of total observations falling within each interval.
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Subject 3. Frequency Distributions;
The relative frequency for a class is calculated by dividing the number of observations in a class by the total number of observations and converting this figure to a percentage (multiplying the fraction by 100). <span>Simply, relative frequency is the percentage of total observations falling within each interval. It is another way of analyzing data; it tells us, for each class, what proportion (or percentage) of data falls in that class.
Let's look at an example.
The fo
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#reading-9-probability-concepts
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#reading-8-statistical-concepts-and-market-returns
Question
Cual es el acrónimo para la construccion de una frequecy table?
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Frequency distribution stepsConstruction of a Frequency Distribution.
Sort (in ascending order)
Calculate the range (Range = Maximum value − Minimum value)
Intervals creation (decide the number you will put in the frequency distribution, k.)
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#reading-8-statistical-concepts-and-market-returns
Question
Construction of a Frequency Distribution.
-
S [...]
-
C [...]
Answer
Sort (in ascending order)
Calculate the range
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Frequency distribution stepsConstruction of a Frequency Distribution.
Sort (in ascending order)
Calculate the range (Range = Maximum value − Minimum value)
Intervals creation (decide the number you will put in the frequency distribution, k.)
Width determination ( interval width = Range/k.)
Ad
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#statistical-concepts-and-market-returns
Question
The letter k represents [...]
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#reading-8-statistical-concepts-and-market-returns
Question
In investments, what do we use to average a time series of rates of return on an asset or a portfolio?
Answer
we use the geometric
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#reading-8-statistical-concepts-and-market-returns
Question
Quantiles that divide a distribution into four equal parts.
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#reading-8-statistical-concepts-and-market-returns
Question
Quantiles that divide a distribution into 100 equal parts.
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#reading-8-statistical-concepts-and-market-returns
Question
Given a set of observations, how many observations lie below the 33th percentile?
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#reading-8-statistical-concepts-and-market-returns
Question
Using [...] we move the percent of the distance above the integer (e.g 12.75-12= 75%) from X12 to X13 as an estimate of Py.
Answer
linear interpolation
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#reading-8-statistical-concepts-and-market-returns
Question
The interquartile range, focuses on [...] rather than [...] .
Answer
The middle
the extremes
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Interquartile RangeAnother distance measure of dispersion that we may encounter, the interquartile range, focuses on the middle rather than the extremes. The interquartile range (IQR) is the difference between the third and first quartiles of a data set: IQR = Q 3 − Q 1 . The IQR represents the length of the interval containing the mi
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#reading-8-statistical-concepts-and-market-returns
Answer
Semistandard deviation
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#reading-8-statistical-concepts-and-market-returns
Question
For asymmetric distributions, variance and semivariance rank [...]
Answer
prospects’ risk differently
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#reading-8-statistical-concepts-and-market-returns
Question
the coefficient of variation is a [...] measure
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#reading-8-statistical-concepts-and-market-returns
Question
A higher coefficient of variation means that sample has [...] than the other sample.
Answer
greater variability (dispersion) in whatever is being measured
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#reading-8-statistical-concepts-and-market-returns
Question
skewness is computed using [...]
Answer
each observation’s deviation from its mean
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#reading-8-statistical-concepts-and-market-returns
Question
Excess Kurtosis formula
\(K_e =\) [...] \( \displaystyle\sum_{i=1}^n(Xi-\bar{X})^4\over {s^4} \)\(- {3(n-1)^2\over (n-2)(n-3)}\)
Answer
\(Ke = {n(n+1) \over (n-1)(n-2)(n-3)}\)
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#reading-9-probability-concepts
Question
To understand the meaning of a probability in investment contexts, we need to distinguish between two types of probability: [...]
Answer
unconditional and conditional.
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Question
To find quantiles in a frequency distribution you have to know [...]
Answer
cumulative frequency
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#reading-8-statistical-concepts-and-market-returns
Question
Dispersion can be also called [...]
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Question
Con que letras se representa la desviación estandar de una muestra?
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#reading-8-statistical-concepts-and-market-returns
Question
Excess Kurtosis formula
\(Ke = {n(n+1) \over (n-1)(n-2)(n-3)}\) * \( {\displaystyle\sum_{i=1}^{n} (x_i-\bar{x})^4 \over s^4}\) - [...]
Answer
\(- {3(n-1)^2 \over (n-2)(n-3)}\)
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In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment. A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set.
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#reading-9-probability-concepts
Question
the [...] of an experiment or random trial is the set of all possible outcomes or results of that experiment.
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#reading-9-probability-concepts
Question
Can probabilities be negative?
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#reading-9-probability-concepts
Question
A set of possible outcomes is just [...]
Answer
Just a list of the outcomes
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Article 1645238684940Lesson 1. Sample space #edx-probability
Putting together a probabilistic Model that is, a model of a random
phenomenon or a random experiment involves two steps.
First step, we describe the possible outcomes of the phenomenon or experiment
of interest.
Second step, we describe our beliefs about the likelihood of the different possible outcomes by specifying a probability law.
Here, we start by just talking about the first step, namely, the description of the possible outcomes of the experiment.
So we carry out an experiment. For example, we flip a coin. Or maybe we flip five coins simultaneously.
Or maybe we roll a die.
Whatever that experiment is,
it has a number of possible
outcomes, and we start
by making a list of
the possible outcomes--
or, a better word, instead of
the word "list", is to use the
word "set", which has a more
formal mathematical meaning.
So we create a set
that we usually
denote by capital omega.
That set is called the sample
space and is the set of all
possible outcomes of
our
Question
A [...] is a model of a random phenomenon or a random experiment
Answer
probabilistic Model
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Lesson 1. Sample space Putting together a probabilistic Model that is, a model of a random
phenomenon or a random experiment involves two steps.
First step, we describe the possible outcomes of the phenomenon or experiment
of interest.
Second step, we describe our beliefs about the
A mathematical model is a description of a system using mathematical concepts and language.
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model+definition+mathematics - Buscar con Googlehttps://en.wikipedia.org/wiki/Mathematical_model","th":120,"tu":"https://encrypted-tbn0.gstatic.com/images?q\u003dtbn:ANd9GcSuTdVRcwZOxMfups7ajRrrK7-0wG9HlGQMOjH29i6tYgAjzXEg6rJKMUgH","tw":200} <span>A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. ... A model may help to explain a system and to study the effects of different components, and to make pr
Question
Putting together a probabilistic Model involves two steps:
First step, we describe the [...]
Second step, we describe [...]
Answer
possible outcomes of the phenomenon or experiment
our beliefs about the likelihood of the different possible outcomes
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Lesson 1. Sample space Putting together a probabilistic Model that is, a model of a random
phenomenon or a random experiment involves two steps.
First step, we describe the possible outcomes of the phenomenon or experiment
of interest.
Second step, we describe our beliefs about the likelihood of the different possible outcomes by specifying a probability law.
Here, we start by just talking about the first step, namely, the description of the possible outcomes of the experiment.
So we carry out an experiment. For example
Question
An experiment has a number of possible outcomes,when we make a list of them we call it a [...]
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Lesson 1. Sample space e first step, namely, the description of the possible outcomes of the experiment.
So we carry out an experiment. For example, we flip a coin. Or maybe we flip five coins simultaneously.
Or maybe we roll a die.
<span>Whatever that experiment is,
it has a number of possible
outcomes, and we start
by making a list of
the possible outcomes--
or, a better word, instead of
the word "list", is to use the
word "set", which has a more
formal mathematical meaning.
So we create a set
that we usually
denote by capital omega.
That set is called the sample
Question
A set of outcomes in an experiment is denoted by [...]
Answer
\(\Omega\)
Capital omega
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Lesson 1. Sample space ng a list of
the possible outcomes--
or, a better word, instead of
the word "list", is to use the
word "set", which has a more
formal mathematical meaning.
So we create <span>a set
that we usually
denote by capital omega.
That set is called the sample
space and is the set of all
possible outcomes of
our experiment.
The elements of that set
should have certa
Question
A set of all possible outcomes of an experiment is called [...]
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Lesson 1. Sample space rd, instead of
the word "list", is to use the
word "set", which has a more
formal mathematical meaning.
So we create a set
that we usually
denote by capital omega.
<span>That set is called the sample
space and is the set of all
possible outcomes of
our experiment.
The elements of that set
should have certain
properties.
Namely, the elements should
be mutually exclusive and
collectively exhaust
#edx-probability
The elements of a sample space should be mutually exclusive and collectively exhaustive.
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Lesson 1. Sample space ematical meaning.
So we create a set
that we usually
denote by capital omega.
That set is called the sample
space and is the set of all
possible outcomes of
our experiment.
<span>The elements of that set
should have certain
properties.
Namely, the elements should
be mutually exclusive and
collectively exhaustive.
What does that mean?
Mutually exclusive means that,
if at the end of the
experiment, I tell you that this
outcome happened, then it
shoul
#edx-probability
Whenever you put together a
model, you need to decide how
detailed you want your model to be. And the right level of detail is
the one that captures those aspects that are relevant and of interest to you.
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Lesson 1. Sample space rder to play with
that theory, or maybe check it
out, and so on, then, in such
a case, you might want to work
with the second sample space.
This is a common feature
in all of science.
<span>Whenever you put together a
model, you need to decide how
detailed you want your model to be. And the right level of detail is
the one that captures those aspects that are relevant and of interest to you.<span><body><html>
Article 1645261753612Lesson 1. Sample space #edx-probability
MITx Video | 6.041x | Spring 2014 | Video transcript | L01-2: Sample space examples
Let us now look at some examples of sample spaces. Sample spaces are sets. And a set can be discrete, finite, infinite, continuous, and so on. Let us start with a simpler case in which we have a sample space that is discrete and finite.
The particular experiment we will be looking at is the following. We take a very special die, a tetrahedral die. So it's a die that has four faces numbered from 1 up 4. We roll it once. And then we roll it twice [again].
Were not dealing here with two probabilistic experiments. We're dealing with a single probabilistic experiment that involves two rolls of the die within that experiment. What is the sample space of that experiment? Well, one possible representation is the following. We take note of the result of the first roll. And then we take note of the result of the second roll. And this gives us a pair of numbers.
Each one of the possible pairs of numbers corresponds to one of th
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Lesson 1. Sample space MITx Video | 6.041x | Spring 2014 | Video transcript | L01-2: Sample space examples
Let us now look at some examples of sample spaces. Sample spaces are sets. And a set can be discrete, finite, infinite, continuous, and so on. Let us start with a simpler case in which we have a sample space that is discrete and finite.
The particul
Question
[...] can be discrete, finite, infinite, continuous, and so on.
Answer
a set (sample space)
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Lesson 1. Sample space MITx Video | 6.041x | Spring 2014 | Video transcript | L01-2: Sample space examples
Let us now look at some examples of sample spaces. Sample spaces are sets. And a set can be discrete, finite, infinite, continuous, and so on. Let us start with a simpler case in which we have a sample space that is discrete and finite.
The particular experiment we will be looking at is the following. We take a very
#edx-probability
A very useful way of describing the sample space of experiments-- whenever we have an experiment with several stages, either real stages or imagined stages is by providing a sequential description in terms of a tree.
So a diagram of this kind, we call it a tree. You can think of this as the root of the tree from which you start. And the endpoints of the tree, we usually call 1 them the leaves.
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Lesson 1. Sample space comes.
Now this is a case of a model in which the probabilistic experiment can be described in phases or stages. We could think about rolling the die once and then going ahead with the second roll. So we have two stages.
<span>A very useful way of describing the sample space of experiments-- whenever we have an experiment with several stages, either real stages or imagined stages. So a very useful way of describing it is by providing a sequential description in terms of a tree. So a diagram of this kind, we call it a tree. You can think of this as the root of the tree from which you start. And the endpoints of the tree, we usually call 1 them the leaves.
So the experiment starts. We carry out the first phase, which in this case is the first roll. And we see what happens. So maybe we get a 2 in the first roll. And then we take
Why study medieval Arabic praise poetry? To give a straightforward response, this genre is pivotal for anyone interested in the 'Golden Age' of the medieval Near East - a time when Baghdad and Samarra were capitals of a cosmopolitan, if turbulent, civilization, and every person of merit, from lute-player to lexicographer, sought entry to the Abbasid court.
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praise poetry enshrined the Abbasid ruler ideology and its Islamic world-view.
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The high visibility of madf~ can be explained by the literary prestige it conferred upon a ruling dynasty - a validation no other cultural practice could confer.
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In medieval Arabic praise, trade lacks intrinsic negative connotations as well as the (modern) distinction between moral and material exchange. The 'usefulness' of madih was not only unobjectionable, it constituted part of this poetry's very value.
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Question
The Arabic term madīḥ is often rendered in English with which two terms?
Answer
'panegyrics' or 'praise poetry,'
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Indeed, madīḥ was much broader than that and included, next to praise, other tones of address ranging from advice and exhortation to criticism, direct accusation, and warning.
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The poet voices two concerns with remarkable directness: he complains about a withheld reward for his poetry (2-3) and accuses his patron of trying to compete with him in poetry (5-12)
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The poet takes his dissatisfaction as an occasion to raise the question of poetic patronage and the function of reward. Ibn al-RiimI also sets clear boundaries between the tasks of sovereign and praise poet and proceeds to lecture his patron about the dos and don 'ts of a sovereign. He distinctly reminds Mul)ammad (or 1Jbaydallah) of his passive role in poetry, that of being a model for depiction (5, 12), as opposed to his active role in imparting mercy and generosity (7-8, 12)
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Arabic poetry is in general characterized by having a purpose, such as to boast, praise, satirize, or describe, and the concept of poetry as 'pure art' and social grace only emerged in the Abbasid period among the dilettante poets from the ruling elite.
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Tags
#reading-9-probability-concepts
Question
Cual era la tonteria que estabas haciendo en probabilidad?
Answer
Multiplicar P (AB) en eventos dependientes
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Article 1645289540876Subject 2. Unconditional, Conditional, and Joint Probabilities#reading-9-probability-concepts
The complement of event A is the event that A does not occur. It is expressed as A c . The probabilities of an event and its complement must have a sum of 1: P(A) + P(A c ) = 1. Note that event A and its complement, A c , are mutually exclusive (there is no overlapping of their possible outcomes) and exhaustive (these two events include all possible outcomes). For example, event A refers to an increase in interest rates. The probability of event A is 0.7. A c is the event that interest rates will not increase. P(A c ) = 1 - 0.7 = 0.3.
Probabilities are either unconditional or conditional.
Unconditional probability, also called marginal probability, is simply the probability of an event occurring. It refers to the probability of an event that is not conditioned on the occurrence of another event. For example, what is the probability that a stock earns a return above the risk-free rate? An unconditional probability can be considered as a stand-alone probability. It is expressed as P(A).
Tags
#reading-9-probability-concepts
Question
The complement of event A is [...]
Answer
the event that A does not occur.
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Subject 2. Unconditional, Conditional, and Joint Probabilities
The complement of event A is the event that A does not occur. It is expressed as A c . The probabilities of an event and its complement must have a sum of 1: P(A) + P(A c ) = 1. Note that event A and its complement, A c , are mutually exclusive (t
Tags
#reading-9-probability-concepts
Question
The [...] is expressed as Ac
Answer
complement of event A
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Subject 2. Unconditional, Conditional, and Joint Probabilities
The complement of event A is the event that A does not occur. It is expressed as A c . The probabilities of an event and its complement must have a sum of 1: P(A) + P(A c ) = 1. Note that event A and its complement, A c , are mutually exclusive (there is no overlapping
Tags
#reading-9-probability-concepts
Question
The expression to the left of the vertical bar represents [...] and the expression to the right of the vertical bar represents [...]
Answer
the event
the condition.
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Subject 2. Unconditional, Conditional, and Joint Probabilities total more than 8 (6,3; 6,4; 6,5; 6,6). The probability of a total greater than 8, given that the first dice is 6, is therefore 4/6 = 2/3. More formally, this probability can be written as: P(total>8 | Dice 1 = 6) = 2/3. In this equation, <span>the expression to the left of the vertical bar represents the event and the expression to the right of the vertical bar represents the condition. Thus, it would be read as "The probability that the total is greater than 8, given that Dice 1 is 6, is 2/3." In more abstract form, P(A|B) is the probability of event A given
Tags
#reading-9-probability-concepts
Question
multiplication rule for probabilities:
Answer
P(AB) = P(A|B) x P(B)
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Subject 2. Unconditional, Conditional, and Joint Probabilitiesnction of two random variables, X and Y, gives the probability of joint occurrences of the values of X and Y.
If we know the conditional probability P(A|B) and we want to know the joint probability P(AB), we can use the following <span>multiplication rule for probabilities:
P(AB) = P(A|B) x P(B)
Example 1
If someone draws a card at random from a deck and then, without replacing the first card, draws a second card, what is the probability that both card
#reading-9-probability-concepts
Look out for the words "given that" or "you are told that," which will help you know that the probability is conditional. In the absence of such information, the probability will be unconditional.
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Subject 2. Unconditional, Conditional, and Joint Probabilitiesoil price, P(B), is 0.4. The probability of an increase in airfare given an increase in oil price, P(A|B), is 0.3. The joint probability of an increase in both oil price and airfare, P(AB), is 0.3 x 0.4 = 0.12.
Hint:
<span>Look out for the words "given that" or "you are told that," which will help you know that the probability is conditional. In the absence of such information, the probability will be unconditional. The letter after the | is the event that we know has definitely occurred, whereas the letter before the | is the event whose probability we are trying to calculate.
<span>
#reading-9-probability-concepts
The letter after the | is the event that we know has definitely occurred, whereas the letter before the | is the event whose probability we are trying to calculate.
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Subject 2. Unconditional, Conditional, and Joint Probabilities
Hint:
Look out for the words "given that" or "you are told that," which will help you know that the probability is conditional. In the absence of such information, the probability will be unconditional. <span>The letter after the | is the event that we know has definitely occurred, whereas the letter before the | is the event whose probability we are trying to calculate.
<span><body><html>