The President is indirectly elected: they are selected by members of the Parliament of India (both houses) and the Legislative Assemblies of each of India's states and territories

The office-holder serves for a term of five years; there are no term limits

The oath of the President is taken in the presence of the Chief Justice of India, and in his/her absence, by the most senior judge of the Supreme Court of India

The Protection of Children from Sexual Offences Act, 2012

Definition of a child under the Act: The Act is gender-neutral and defines a child as any person below the age of eighteen years.

The Protection of Children from Sexual Offences Act, 2012 provides:

1. Precise definitions for different types of Child abuse crimes
2. Stringent punishments
3. Mandatory reporting
4. Child-friendly procedures
5. Under Section 45 of the Act, the power to make rules rests with the Central Government
6. Qualifications and experience of interpreters
7. Arrangements for care and protection
8. Criteria for award of compensation by the Special Court
9. The rules rely on the structures established under the Juvenile Justice Act, 2000.

The section 23(2) of the Act specifies that all teachers at elementary level at commencement of this law if did not possess minimum qualifications under it need to acquire these within a period of five years

Education as Fundamental Right:

1. Every Child of the age group of 6-14 years shall have right to free and compulsory Education.
2. No child is liable to pay any kind of fee/ capitation fee/ charges.
3. A collection of capitation fee invites a fine up to 10 times the amount collected.

This right provides that “child belonging to disadvantage group” means a child who

1. Belongs to SC & ST
2. Socially backward class.
3. Geographical, Linguistic, Gender or such other matters.
4. Is differentially abled

India, the world’s largest arms importer, relies on imports to meet more than [...] of its defence requirements So far, technology was imported and the products manufactured at home, at cut-rate prices Currently, the FDI in Defence Sector is capped at [...] and cases for higher FDI are considered on case to case basis

DPP is the governing manual for all defence procurement. It was part of a set of military reforms undertaken to address the many deficiencies noticed during the 1999 Kargil war.

It was launched for the first time in 2002, and since then, DPP has been revised periodically. The DPP 2016 is based on the recommendations of the expert committee headed by former Home Secretary Dhirendra Singh, which submitted its report last year; most of its suggestions are accepted.

What’s new in the DPP 2016?

It seeks to address the concerns of defence manufacturers and suppliers and enhanced transparency.

• Included a new category to acquire weapons–IDDM (Indigenously Designed, Developed and Manufactured). IDDM will be the first preferred category of preference
• A 10% weightage has been introduced for superior technology, instead of selecting the lowest bidder only in financial terms
• Govt funding for R&D and recognition of the MSME in technology development
• Defence Acquisition Council to take a “fast-track” route to acquire weapons, something which was limited to only armed forces till now
• Defence export clearances will now be granted online

What are the important categories in the policy?

• Buy (Indian-IDDM) : At least 40% of a product must be manufactured in India for it to qualify for the Indian Designed, Developed and Manufactured category. If the equipment is not indigenously designed, but constitutes 60% indigenous content on cost basis of total contract value. This will be also accorded priority. This category will be preferred to vendors offering equipment designed abroad
• Buy (Indian): An equipment from Indian vendors could be procured, only if it comprises of a minimum of 40% indigenous content on cost basis of the total contract value
• Make category: Make-I category utilises critical technologies and involves huge infrastructure investment; on the other hand, Make-II category entails use of commercial, military or even dual-use technologies, and is operated on a smaller scale. It seeks to promote SMEs

Why it is necessary to go for Indigenisation of defence equipments?

First of all, India has all the necessary prerequisites for a robust military-industrial complex: a diverse private sector, a large base of engineering institutes, and a growing defence budget.

However, India also faces a combination of security threats from both state and non-state actors is an obvious reason by it needs to be self-reliant in military equipment. It will also significantly reduce the potential for corruption in military procurement.

The move will give fillip to make in India and job creation. It will also bring down dependence on imports.

World Customs Organization

1. The World Customs Organization (WCO) is an intergovernmental organization headquartered in Brussels, Belgium
2. It has 182 member nations (including India) that manage more than 98% of world trade.
3. The WCO is noted for its work in areas covering the development of international conventions, instruments, and tools on topics such as commodity classification, valuation, rules of origin, collection of customs revenue, supply chain security, international trade facilitation, customs enforcement activities, combating counterfeiting in support of Intellectual Property Rights (IPR), drugs enforcement, illegal weapons trading, integrity promotion, and delivering sustainable capacity building to assist with customs reforms and modernization
4. The WCO maintains the international Harmonized System (HS) goods nomenclature, and administers the technical aspects of the World Trade Organization (WTO) Agreements on Customs Valuation and Rules of Origin

Trade Facilitation Agreement (TFA)

1. The TFA is the WTO’s first-ever multilateral accord that aims to simplify customs regulations for the cross-border movement of goods. It was outcome of WTO’s 9th Bali (Indonesia) ministerial package of 2013
2. The agreement includes provisions for Lowering import tariffs and agricultural subsidies: It will make it easier for developing countries to trade with the developed world in global markets
3. Abolish hard import quotas: Developed countries would abolish hard import quotas on agricultural products from the developing world and instead would only be allowed to charge tariffs on amount of agricultural imports exceeding specific limits
4. Reduction in red tape at international borders: It aims to reduce red-tapism to facilitate trade by reforming customs bureaucracies and formalities

The first rule of Janki boosts your memory:
“Every time you learn something new create a question and answer flashcard and add this card to Anki.”

The second rule of Janki encourages a commitment to daily learning:
“You must use Anki every single day - including weekends and holidays - and commit to doing so indefinitely.”

The third rule of Janki keeps you focused on what is important in the moment:
“Learn in context. Pick a project, and learn only what you need to get it done.”

The fourth rule of Janki grounds knowledge in reality:
“Only add a card to your deck after having tried to use the item of knowledge therein.”

The fifth rule of Janki method minimizes mistake repetition.
“Every time you make a mistake carry out a post-mortem and try to figure out the lessons in the experience. Think about what you would need to know to prevent that mistake from occurring again, and turn this insight into new flashcards.”

The sixth rule of Janki method encourages regular critical reflection:
“At the end of every project ask yourself what lessons you learned and what you would do differently if you were to repeat the project with the benefit of hindsight.”

The seventh rule of Janki keeps your decks in shape.
“Delete or modify any incorrect, outdated, difficult to remember, incomplete or unnecessary cards. Update existing cards as improved understanding dawns.”

The eighth rule of Janki encourages you to use your readings of other people’s code as a source of learning:
“Read the subject regularly. If you come across something interesting create a card detailing the technique.”

Construction of a Frequency Distribution.

1. Sort (in ascending order)

2. Calculate the range (Range = Maximum value − Minimum value)

3. Intervals creation (decide the number you will put in the frequency distribution, k.)

4. Width determination ( interval width = Range/k.)

5. Add the interval width to the minimum value (stop after reaching an interval that includes the maximum value)

6. Count (the number of observations in each interval)

7. Table (make a table of intervals from small to large that shows the number of observations in each one)

Although some guidelines for setting k have been suggested in statistical literature, the setting of a useful value for k often involves inspecting the data and exercising judgment. How much detail should we include? If we use too few intervals, we will summarize too much and lose pertinent characteristics. If we use too many intervals, we may not summarize enough.

The notation M_d is occasionally used for the median. Just as for the mean, we may distinguish between a population median and a sample median. With the understanding that a population median divides a population in half while a sample median divides a sample in half, we follow general usage in using the term “median” without qualification, for the sake of brevity.

Whether we use the calculation for an even- or odd-numbered sample, an equal number of observations lie above and below the median.

The arithmetic mean is a special case of the weighted mean in which all the weights are equal to 1/n.

Now suppose that the portfolio manager maintains constant weights of 60 percent in stocks and 40 percent in bonds for all five years. This method is called a constant-proportions strategy. Because value is price multiplied by quantity, price fluctuation causes portfolio weights to change. As a result, the constant-proportions strategy requires rebalancing to restore the weights in stocks and bonds to their target levels. Assuming that the portfolio manager is able to accomplish the necessary rebalancing, we can compute the portfolio returns in 2009, 2010, 2011, and 2012 with Equation 4 as follows:

Portfolio return for 2009 = 0.60(34.1) + 0.40(11.0) = 24.9%

Portfolio return for 2010 = 0.60(16.8) + 0.40(6.4) = 12.6%

Portfolio return for 2011 = 0.60(–9.2) + 0.40(8.4) = –2.2%

Portfolio return for 2012 = 0.60(6.4) + 0.40(3.8) = 5.4%

We can now find the time-series mean of the returns for 2008 through 2012 using Equation 3 for the arithmetic mean. The time-series mean total return for the portfolio is (−19.9 + 24.9 + 12.6 − 2.2 + 5.4)/5 = 20.8/5 = 4.2 percent.

Instead of calculating the portfolio time-series mean return from portfolio annual returns, we can calculate the arithmetic mean stock and bond fund returns for the five years and then apply the portfolio weights of 0.60 and 0.40, respectively, to those values. The mean stock fund return is (−33.1 + 34.1 + 16.8 − 9.2 + 6.4)/5 = 15.0/5 = 3.0 percent. The mean bond fund return is (−0.1 + 11.0 + 6.4 + 8.4 + 3.8)/ 5 = 29.5/5 = 5.9 percent. Therefore, the mean total return for the portfolio is 0.60(3.0) + 0.40(5.9) = 4.2 percent, which agrees with our previous calculation.

Suppose we make one forecast for the year-end level of the S&P 500 assuming economic expansion and another forecast for the year-end level of the S&P 500 assuming economic contraction. If we multiply the first forecast by the probability of expansion and the second forecast by the probability of contraction and then add these weighted forecasts, we are calculating the expected value of the S&P 500 at year-end. If we take a weighted average of possible future returns on the S&P 500, we are computing the S&P 500’s expected return.

A hypothetical investment in a single stock initially costs €100. One year later, the stock is trading at €200. At the end of the second year, the stock price falls back to the original purchase price of €100. No dividends are paid during the two-year period. Calculate the arithmetic and geometric mean annual returns.

Solution:

First, we need to find the Year 1 and Year 2 annual returns with Equation 1.

Return in Year 1 = 200/100 – 1 = 100%

Return in Year 2 = 100/200 – 1 = –50%

The arithmetic mean of the annual returns is (100% − 50%)/2 = 25%.

Before we find the geometric mean, we must convert the percentage rates of return to (1 + R_t). After this adjustment, the geometric mean from Equation 6 is √2.0×0.502.0×0.50 – 1 = 0 percent.

The geometric mean return of 0 percent accurately reflects that the ending value of the investment in Year 2 equals the starting value in Year 1. The compound rate of return on the investment is 0 percent. The arithmetic mean return reflects the average of the one-year returns.

The terminology “harmonic” in Harmonic Mean arises from its use relative to a type of series involving reciprocals known as a harmonic series.

The harmonic mean is a relatively specialized concept of the mean that is appropriate when averaging ratios (“amount per unit”) when the ratios are repeatedly applied to a fixed quantity to yield a variable number of units.

Dollar-cost averaging (DCA) is an investment technique of buying a fixed dollar amount of a particular investment on a regular schedule, regardless of the share price. The investor purchases more shares when prices are low and fewer shares when prices are high. The premise is that DCA lowers the average share cost over time, increasing the opportunity to profit. The DCA technique does not guarantee that an investor won't lose money on investments. Rather, it is meant to allow investment over time instead of investment as a lump sum.

What are the reasons for sampling?

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Sampling is used when:

1. The population is infinite.
2. There is a limited amount of time available.
3. The nature of the test is destructive.
4. The cost of gathering the data is a factor.

When dealing with actual data, we often find that we need to approximate the value of a percentile. For example, if we are interested in the value of the 75th percentile, we may find that no observation divides the sample such that exactly 75 percent of the observations lie at or below that value. The following procedure, however, can help us determine or estimate a percentile. The procedure involves first locating the position of the percentile within the set of observations and then determining (or estimating) the value associated with that position.