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Consider the multiplicative model X t = m t × s t × W t .Let Y t denote the time series of logarithms: Y t =log X t .Then Y t =log X t Y t = log(m t × s t × W t ) Y t = log m t +log s t +log W t .

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if a multiplicative model is appropriate for the time series X t , then an additive model is appropriate for the time series of logarithms, Y t =log X t .

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if a multiplicative model is appropriate for the time series X t , then an additive model is appropriate for the time series of logarithms, Y t =log X t .

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if a multiplicative model is appropriate for the time series X t , then an additive model is appropriate for the time series of logarithms, Y t =log X t .

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by taking logarithms, a time series for which a multiplicative model is appropriate can be transformed into a time series for which an additive model is appropriate.

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Transformations of time series that are commonly used include the power transformations: Y t = X t a , where a = ... 1/4, 1/3, 2, 3, 4, ....

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Transformations of time series that are commonly used include the power transformations: Y t = X t a , where a = ... 1/4, 1/3, 2, 3, 4, ....

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A simple moving average (or just a moving average) of order (or span) 11 can be written as Y t = 111(X t−5 + ···+ X t + ···+ X t+5 )

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A simple moving average (or just a moving average) of order (or span) 11 can be written as Y t = 111(X t−5 + ···+ X t + ···+ X t+5 )

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A simple moving average (or just a moving average) of order (or span) 11 can be written as Y t = 111(X t−5 + ···+ X t + ···+ X t+5 )

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For the purpose of smoothing time series, only moving averages for which the order is an odd number will be used. These are said to be centred on the middle value.

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With a suitable degree of smoothing — that is, with a suitable choice of the order of the moving average — the moving average provides an estimate of the trend component m t ; this is denoted mt^

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A weighted moving average of order 2q + 1 has the form MA(t)= a −q X t−q + ···+ a −1 X t−1 + a 0 X t + a 1 X t+1 + ···+ a q X t+q , where the weights a j , j = −q, −q +1,... ,

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A weighted moving average of order 2q + 1 has the form MA(t)= a −q X t−q + ···+ a −1 X t−1 + a 0 X t + a 1 X t+1 + ···+ a q X t+q , where the weights a j , j = −q, −q +1,... ,q, add up to 1.</

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A weighted moving average of order 2q + 1 has the form MA(t)= a −q X t−q + ···+ a −1 X t−1 + a 0 X t + a 1 X t+1 + ···+ a q X t+q , where the weights a j , j = −q, −q +1,... ,q, add up to 1.

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l>A weighted moving average of order 2q + 1 has the form MA(t)= a −q X t−q + ···+ a −1 X t−1 + a 0 X t + a 1 X t+1 + ···+ a q X t+q , where the weights a j , j = −q, −q +1,... ,q, add up to 1.<html>

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The weighted moving averages are denoted SA(t) rather than MA(t) when their particular use in smoothing out seasonal variation.

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The weighted moving averages are denoted SA(t) rather than MA(t) when their particular use in smoothing out seasonal variation.

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ead>The ﬁrst step is to ﬁnd an initial estimate of the trend component m t that is not unduly inﬂuenced by the seasonal component s t . A reasonable starting point would be to use a simple moving average with order equal to the period T of the seasonal cycle. Such a moving average would smooth out the seasonal variation, as the annual highs and lows would cancel out.<html>

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The simple moving average is a weighted moving average in which the weights a j are all equal to (2q +1) −1

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One way to predict tomorrow’s average temperature is to assume it will be the same as today’s.

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t level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value at time n, \hat{x}_nand \hat{x}_{n+1}are <span>the 1-step ahead forecasts of X n and X n+1 , and α is a smoothing parameter, 0 ≤ α ≤ 1. The method requires an initial value \hat{x}_1, which is often chosen to be x 1 : \hat{x}_1 = x 1 .<span><body><html>

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e obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value at time n, \hat{x}_nand \hat{x}_{n+1}are the 1-step ahead forecasts of X n and X n+1 , and α is <span>a smoothing parameter, 0 ≤ α ≤ 1. The method requires an initial value \hat{x}_1, which is often chosen to be x 1 : \hat{x}_1 = x 1 .<span><body><html>

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If a time series X t is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where:&

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If a time series X t is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the ob

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If a time series X t is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value

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If a time series X t is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value at time n, \ha

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If a time series X t is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value at time n, \hat{x}_nand \hat{x}_{n+1}are the 1-step ahead forecasts of X n and X n

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If a time series X t is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula \(\hat{x}_{n+1}\)= αx n + (1 − α)\(\hat{x}_n\) where: x n is the observed value at time n, \(\hat{x}_n\)and \(\hat{x}_{n+1}\)are the 1-step ahead forecasts of X n and X n+1 , and α is a smoothing parameter, 0 ≤ α ≤ 1.

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A statistic is defined as a numerical quantity (such as the mean) calculated in a sample.

Estimates of these parameters taken from a sample are called statistics. Much of the field of statistics is devoted to drawing inferences from a sample concerning the value of a population parameter. <span>A statistic is defined as a numerical quantity (such as the mean) calculated in a sample. It has two different meanings. Most commonly, statistics refers to numerical data such as a company's earnings per share or average returns over the past five years. Statistics can also refer to the process of collecting, organizing, presenting, analyzing, and interpreting numerical data for the purpose of making decisions. Note that we will always know the exact composition of our sample, and by definition, we will always know the values within our sample. Ascertaining this information is the purpose of samples. Sample statistics will always be known, and can be used to estimate unknown population parameters. Hint: One way to easily remember these terms is to recall that "population" and "parameter" both start with a "p," and "sample" and "statisti

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A statistic is defined as a numerical quantity (such as the mean) calculated in a sample.

Estimates of these parameters taken from a sample are called statistics. Much of the field of statistics is devoted to drawing inferences from a sample concerning the value of a population parameter. <span>A statistic is defined as a numerical quantity (such as the mean) calculated in a sample. It has two different meanings. Most commonly, statistics refers to numerical data such as a company's earnings per share or average returns over the past five years. Statistics can also refer to the process of collecting, organizing, presenting, analyzing, and interpreting numerical data for the purpose of making decisions. Note that we will always know the exact composition of our sample, and by definition, we will always know the values within our sample. Ascertaining this information is the purpose of samples. Sample statistics will always be known, and can be used to estimate unknown population parameters. Hint: One way to easily remember these terms is to recall that "population" and "parameter" both start with a "p," and "sample" and "statisti

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the order of the different scales is NOIR (the French word for black)

ey. Both examples can be measured on a zero scale, where zero represents no return, or in the case of money, no money. Note that as you move down through this list, the measurement scales get stronger. <span>Hint: Remember the order of the different scales by remembering NOIR (the French word for black); the first letter of each word in the scale is indicated by the letters in the word NOIR. Before we move on, here's a quick exercise to make sure that you understand the different measurement scales. In each case, identify whether you think the data is nominal, ordinal, inter

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A parameter is a numerical quantity measuring some aspect of a population of scores.

ve values associated with them, such as the average of all values in a sample and the average of all population values. Values from a population are called parameters, and values from a sample are called statistics. <span>A parameter is a numerical quantity measuring some aspect of a population of scores. The mean, for example, is a measure of central tendency. Greek letters are used to designate parameters. Parameters are rarely known and are usually estimated by statistics computed in samples. Populations can have many parameters, but investment analysts are usually only concerned with a few, such as the mean return or the standard deviation of returns. Estimates of these parameters taken from a sample are called statistics. Much of the field of statistics is devoted to drawing inferences from a sample concerning the value of a population parameter. A statistic is defined as a numerical quantity (such as the mean) calculated in a sample. It has two different meanings. Most commonly, statistics refers to

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A parameter is a numerical quantity measuring some aspect of a population of scores.

ve values associated with them, such as the average of all values in a sample and the average of all population values. Values from a population are called parameters, and values from a sample are called statistics. <span>A parameter is a numerical quantity measuring some aspect of a population of scores. The mean, for example, is a measure of central tendency. Greek letters are used to designate parameters. Parameters are rarely known and are usually estimated by statistics computed in samples. Populations can have many parameters, but investment analysts are usually only concerned with a few, such as the mean return or the standard deviation of returns. Estimates of these parameters taken from a sample are called statistics. Much of the field of statistics is devoted to drawing inferences from a sample concerning the value of a population parameter. A statistic is defined as a numerical quantity (such as the mean) calculated in a sample. It has two different meanings. Most commonly, statistics refers to

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The arithmetic mean is what is commonly called the average.

; The sample mean is the average for a sample. It is a statistic and is used to estimate the population mean. where n = the number of observations in the sample <span>Arithmetic Mean The arithmetic mean is what is commonly called the average. The population mean and sample mean are both examples of the arithmetic mean. If the data set encompasses an entire population, the arithmetic mean is called a population mean. If the data set includes a sample of values taken from a population, the arithmetic mean is called a sample mean. This is the most widely used measure of central tendency. When the word "mean" is used without a modifier, it can be assumed to refer to the arithmetic mean. The mean is the sum of all scores divided by the number of scores. It is used to measure the prospective (expected future) performance (return) of an investment over a number of periods. All interval and ratio data sets (e.g., incomes, ages, rates of return) have an arithmetic mean. All data values are considered and included in the arithmetic mean computation. A data set has only one arithmetic mean. This indicates that the mean is unique. The arithmetic mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero. Deviation from the arithmetic mean is the distance between the mean and an observation in the data set. The arithmetic mean has the following disadvantages: The mean can be affected by extremes, that is, unusually large or small values. The mean cannot be determined for an open-ended data set (i.e., n is unknown). Geometric Mean The geometric mean has three important properties: It exists only if all the observations are gre

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The population mean and sample mean are both examples of the arithmetic mean.

; The sample mean is the average for a sample. It is a statistic and is used to estimate the population mean. where n = the number of observations in the sample <span>Arithmetic Mean The arithmetic mean is what is commonly called the average. The population mean and sample mean are both examples of the arithmetic mean. If the data set encompasses an entire population, the arithmetic mean is called a population mean. If the data set includes a sample of values taken from a population, the arithmetic mean is called a sample mean. This is the most widely used measure of central tendency. When the word "mean" is used without a modifier, it can be assumed to refer to the arithmetic mean. The mean is the sum of all scores divided by the number of scores. It is used to measure the prospective (expected future) performance (return) of an investment over a number of periods. All interval and ratio data sets (e.g., incomes, ages, rates of return) have an arithmetic mean. All data values are considered and included in the arithmetic mean computation. A data set has only one arithmetic mean. This indicates that the mean is unique. The arithmetic mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero. Deviation from the arithmetic mean is the distance between the mean and an observation in the data set. The arithmetic mean has the following disadvantages: The mean can be affected by extremes, that is, unusually large or small values. The mean cannot be determined for an open-ended data set (i.e., n is unknown). Geometric Mean The geometric mean has three important properties: It exists only if all the observations are gre

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the arithmetic mean is the most widely used measure of central tendency.

; The sample mean is the average for a sample. It is a statistic and is used to estimate the population mean. where n = the number of observations in the sample <span>Arithmetic Mean The arithmetic mean is what is commonly called the average. The population mean and sample mean are both examples of the arithmetic mean. If the data set encompasses an entire population, the arithmetic mean is called a population mean. If the data set includes a sample of values taken from a population, the arithmetic mean is called a sample mean. This is the most widely used measure of central tendency. When the word "mean" is used without a modifier, it can be assumed to refer to the arithmetic mean. The mean is the sum of all scores divided by the number of scores. It is used to measure the prospective (expected future) performance (return) of an investment over a number of periods. All interval and ratio data sets (e.g., incomes, ages, rates of return) have an arithmetic mean. All data values are considered and included in the arithmetic mean computation. A data set has only one arithmetic mean. This indicates that the mean is unique. The arithmetic mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero. Deviation from the arithmetic mean is the distance between the mean and an observation in the data set. The arithmetic mean has the following disadvantages: The mean can be affected by extremes, that is, unusually large or small values. The mean cannot be determined for an open-ended data set (i.e., n is unknown). Geometric Mean The geometric mean has three important properties: It exists only if all the observations are gre

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nalysis, we can examine whether the data are well described by the most credible possibilities in the considered set. If the data seem not to be well described, then we can consider expanding the set of possibilities. This process is called a <span>posterior predictive check<span><body><html>

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y>In general, data analysis begins with a family of candidate descriptions for the data. The descriptions are mathematical formulas that characterize the trends and spreads in the data. The formulas themselves have numbers, called parameter values, that determine the exact shape of mathematical forms.<body><html>

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The first idea is that Bayesian inference is reallocation of credibility across possibilities.

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The second foundational idea is that the possibilities, over which we allocate credibility, are parameter values in meaningful mathematical models.

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Because we assume that the candidate causes are mutually exclusive and exhaust all possible causes, the total credibility across causes sums to one.

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The distribution of credibility initially reflects prior knowledge about the possibilities, which can be quite vague. Then new data are observed, and the credibility is re-allocated. Possibilities that are consistent with the data garner more credibility, while possibilities

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You can think of parameters as control knobs on mathematical devices that simulate data generation.

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You can think of parameters as control knobs on mathematical devices that simulate data generation.

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The mathematical formula for the normal distribution converts the parameter values to a particular bell-like shape for the probabilities of data values

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The second desideratum for a mathematical description is that it should be descrip- tively adequate, which means, loosely, that the mathematical form should “look like” the data.

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The second desideratum for a mathematical description is that it should be descrip- tively adequate, which means, loosely, that the mathematical form should “look like” the data.

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Bayesian analysis is very useful for assessing the relative credibility of different candidate descriptions of data

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In general, Bayesian analysis of data follows these steps: 1. Identify the data relevant to the research questions. What are the measurement scales of the data? Which data variables are to be predicted, and which data variables are supposed to act as predictors? 2. Define a descriptive model for the relevant data. The mathematical form and its parameters should be meaningful and appropriate to the theoretical purposes of the analysis. 3. Specif

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alysis of data follows these steps: 1. Identify the data relevant to the research questions. What are the measurement scales of the data? Which data variables are to be predicted, and which data variables are supposed to act as predictors? 2. <span>Define a descriptive model for the relevant data. The mathematical form and its parameters should be meaningful and appropriate to the theoretical purposes of the analysis. 3. Specify a prior distribution on the parameters. The prior must pass muster with the audience of the analysis, such as skeptical scientists. 4. Use Bayesian inference to re-allocate c

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ed, and which data variables are supposed to act as predictors? 2. Define a descriptive model for the relevant data. The mathematical form and its parameters should be meaningful and appropriate to the theoretical purposes of the analysis. 3. <span>Specify a prior distribution on the parameters. The prior must pass muster with the audience of the analysis, such as skeptical scientists. 4. Use Bayesian inference to re-allocate credibility across parameter values. Interpret the posterior distribution with respect to theoretically meaningful issues (assuming that the mod

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its parameters should be meaningful and appropriate to the theoretical purposes of the analysis. 3. Specify a prior distribution on the parameters. The prior must pass muster with the audience of the analysis, such as skeptical scientists. 4. <span>Use Bayesian inference to re-allocate credibility across parameter values. Interpret the posterior distribution with respect to theoretically meaningful issues (assuming that the model is a reasonable description of the data; see next step). 5. Check that the posterior predictions mimic the data with reasonable accuracy (i.e., conduct a “posterior predictive check”). If not, then consider a different descriptive model

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e Bayesian inference to re-allocate credibility across parameter values. Interpret the posterior distribution with respect to theoretically meaningful issues (assuming that the model is a reasonable description of the data; see next step). 5. <span>Check that the posterior predictions mimic the data with reasonable accuracy (i.e., conduct a “posterior predictive check”). If not, then consider a different descriptive model<span><body><html>

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One way to summarize the uncertainty is by marking the span of values that are most credible and cover 95% of the distribution. This is called the highest density inter val (HDI) and is marked by the black bar on the floor of the distribution in Figure 2.5.

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Bayesian analysis re- allocates credibility among parameter values within a meaningful space of possibilities defined by the chosen model.

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The standard deviation is another control knob in the mathematical formula for the normal distribution that controls the width or dispersion of the distribution. The standard deviation is sometimes called a scale parameter.

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o make inferences from data without using a model is a method from NHST called resampling or bootstrapping. These methods compute p values to make decisions, and p values have fundamental logical problems that will be discussed in Chapter 11. <span>These methods also have very limited ability to express degrees of certainty about characteristics of the data, whereas Bayesian methods put expression of uncertainty front and center<span><body><html>

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The mean is a control knob in the mathematical formula for the normal distribution that controls the location of the distribution’s central tendency. The mean is sometimes called a location parameter.

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The mean is a control knob in the mathematical formula for the normal distribution that controls the location of the distribution’s central tendency. The mean is sometimes called a location parameter.

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A matrix is simply a two-dimensional array of values of the same type.

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Whenever we ask about how likely an outcome is, we always ask with a set of possible outcomes in mind. This set exhausts all possible outcomes, and the outcomes are all mutually exclusive. This set is called the sample space

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Many coins minted by governments have the picture of an important person’s head on one side. This side is called “heads” or, technically, the “obverse.”

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An array is a generalization of a matrix to multiple dimensions

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One case of trying to make inferences from data without using a model is a method from NHST called resampling or bootstrapping.

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In general, a probability, whether it’s outside the head or inside the head, is just a way of assigning numbers to a set of mutually exclusive possibilities

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A probability distribution is simply a list of all possible outcomes and their corresponding probabilities

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For continuous outcome spaces, we can discretize the space into a finite set of mutually exclusive and exhaustive “bins.”

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Loosely speaking, the term “mass” refers the amount of stuff in an object. When the stuff is probability and the object is an interval of a scale, then the mass is the proportion of the outcomes in the interval.

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The problem with using intervals, however, is that their widths and edges are arbitrary, and wide intervals are not very precise. Therefore, what we will do is make the intervals infinitesimally narrow, and instead of talking about the infinitesimal probability mass of each infinitesimal interval, we will talk ab

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and wide intervals are not very precise. Therefore, what we will do is make the intervals infinitesimally narrow, and instead of talking about the infinitesimal probability mass of each infinitesimal interval, we will talk about the ratio of <span>the probability mass to the interval width. That ratio is called the probability density.<span><body><html>

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erefore, what we will do is make the intervals infinitesimally narrow, and instead of talking about the infinitesimal probability mass of each infinitesimal interval, we will talk about the ratio of the probability mass to the interval width. <span>That ratio is called the probability density.<span><body><html>

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Your job in answering that question is to provide a number between 0 and 1 that accurately reflects your belief probability. One way to come up with such a number is to calibrate your beliefs relative to other events with clear probabilities

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The probability of a discrete outcome, such as the probability of falling into an interval on a continuous scale, is referred to as a probability mass

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Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on.

, therefore, is not recommended for use as the only measure of central tendency. A further disadvantage of the mode is that many distributions have more than one mode. These distributions are called "multimodal." <span>Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by: The mean, median, and mode are equal in symmetric distributions. The mean is higher than the median in positively skewed distributions and lower than the median in negatively skewed dist

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rs x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. <span>For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by: <span><body><html>

, therefore, is not recommended for use as the only measure of central tendency. A further disadvantage of the mode is that many distributions have more than one mode. These distributions are called "multimodal." <span>Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by: The mean, median, and mode are equal in symmetric distributions. The mean is higher than the median in positively skewed distributions and lower than the median in negatively skewed dist

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Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mea

, therefore, is not recommended for use as the only measure of central tendency. A further disadvantage of the mode is that many distributions have more than one mode. These distributions are called "multimodal." <span>Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by: The mean, median, and mode are equal in symmetric distributions. The mean is higher than the median in positively skewed distributions and lower than the median in negatively skewed dist

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Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mea

, therefore, is not recommended for use as the only measure of central tendency. A further disadvantage of the mode is that many distributions have more than one mode. These distributions are called "multimodal." <span>Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by: The mean, median, and mode are equal in symmetric distributions. The mean is higher than the median in positively skewed distributions and lower than the median in negatively skewed dist

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Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on.

, therefore, is not recommended for use as the only measure of central tendency. A further disadvantage of the mode is that many distributions have more than one mode. These distributions are called "multimodal." <span>Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by: The mean, median, and mode are equal in symmetric distributions. The mean is higher than the median in positively skewed distributions and lower than the median in negatively skewed dist

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When you pass a tuple as the first argument in an assert statement, the assertion always evaluates as true and therefore never fails.

valuate to true. I’ve been bitten by this myself in the past. I wrote a longer article about this specific issue you can check out by clicking here. Alternatively, here’s the executive summary: <span>When you pass a tuple as the first argument in an assert statement, the assertion always evaluates as true and therefore never fails. For example, this assertion will never fail: assert(1 == 2, 'This should fail') This has to do with non-empty tuples always being truthy in Python. If you pass a tuple to an assert stat

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When you pass a tuple as the first argument in an assert statement, the assertion always evaluates as true and therefore never fails.

valuate to true. I’ve been bitten by this myself in the past. I wrote a longer article about this specific issue you can check out by clicking here. Alternatively, here’s the executive summary: <span>When you pass a tuple as the first argument in an assert statement, the assertion always evaluates as true and therefore never fails. For example, this assertion will never fail: assert(1 == 2, 'This should fail') This has to do with non-empty tuples always being truthy in Python. If you pass a tuple to an assert stat

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идений 2.1 По З. Фрейду 2.2 Толкование сновидений К. Юнга 3 «Управление» сновидениями 4 Сновидение в религии 5 Дежавю 6 См. также 7 Примечания 8 Литература Общие сведения[править | править код] <span>Наука, изучающая сон, называется сомнология, сновидения — онейрология. Сновидения считаются связанными с фазой быстрого движения глаз (БДГ). Эта стадия возникает примерно каждые 1,5—2 часа сна, и её продолжительность постепенно удлиняется. Она характеризуе

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Наука, изучающая сон , называется сомнология , сновидения — онейрология .

идений 2.1 По З. Фрейду 2.2 Толкование сновидений К. Юнга 3 «Управление» сновидениями 4 Сновидение в религии 5 Дежавю 6 См. также 7 Примечания 8 Литература Общие сведения[править | править код] <span>Наука, изучающая сон, называется сомнология, сновидения — онейрология. Сновидения считаются связанными с фазой быстрого движения глаз (БДГ). Эта стадия возникает примерно каждые 1,5—2 часа сна, и её продолжительность постепенно удлиняется. Она характеризуе

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Наука, изучающая сон , называется сомнология , сновидения — онейрология .

идений 2.1 По З. Фрейду 2.2 Толкование сновидений К. Юнга 3 «Управление» сновидениями 4 Сновидение в религии 5 Дежавю 6 См. также 7 Примечания 8 Литература Общие сведения[править | править код] <span>Наука, изучающая сон, называется сомнология, сновидения — онейрология. Сновидения считаются связанными с фазой быстрого движения глаз (БДГ). Эта стадия возникает примерно каждые 1,5—2 часа сна, и её продолжительность постепенно удлиняется. Она характеризуе

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