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Which of the following statements relating to correlation and reegression are true?<br>1. The coefficient of correlation is independent of change of origin and scale<br>2. The coefficient of correlation between the two variables is the arithmetic average of the two regression coefficients<br>3. The probable error of the coefficient correlation is 0.6745 times of its standard error<br>4. Coefficient of correlation multiplied by the ratio between the standard deviations of the two variables denotes the slope of the regression line<br>Select the correct answer:

Correct Answer: 1, 3 and 4

Simplify the value of $$\frac{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} \times {\text{0}}{\text{.3}} - {\text{3}} \times 0.9 \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}}}}{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} - 0.9 \times {\text{0}}{\text{.2}} - {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}} - 0.3 \times 0.9}} = ?$$

Which of the following statements are true?
1. The coefficient of rank correlation has the same limits as the Karl Pearson's coefficient of correlation.
2. The coefficient of correlation is independent of the change of origin but not of scale.
3. The covariance between $$X$$ and $$Y$$ is defined as $$\frac{{\sum {xy} }}{n}$$ where, $$x = \left( {X - \overline X } \right),y = \left( {Y - \overline Y } \right)$$      and $$n = $$ no. of paired observations.
4. $${b_{xy}}$$ is called regression coefficient of $$X$$ variable on $$Y$$ variable.
5. If $${b_{xy}}$$ is 0.4 and $${b_{yx}}$$ is 1.6, coefficient of determination would be 0.8.
Select the correct answer:

Statement I The product of coefficient of correlation, standard deviation of variable 'X' and Standard deviation of variable 'Y' gives the measure of covariance between X and Y variables.
Statement II The product of coefficient of correlation between X and Y variables and the ratio between standard deviation of X variable to standard deviation of Y variable measures the slope of the regression line of X on Y variable.

$$\frac{{38 \times 38 \times 38 + 34 \times 34 \times 34 + 28 \times 28 \times 28 - 38 \times 34 \times 84}}{{38 \times 38 + 34 \times 34 + 28 \times 28 - 38 \times 34 - 34 \times 28 - 38 \times 28}}$$            is equal to = ?

The following are the two statements relating to the theory of probability. Indicate the statements being correct or incorrect.
Statement I The probability of the joint occurrence of independent events A and B is equal to the probability of event A multiplied by the probability of event B or vice-versa.
Statement II The probability of the joint occurrence of independent event A and dependent event B is equal to the probability of event A multiplied by the conditionalprobability of event B when event A has occurredor vice-versa.

A passage is given with five questions following it. Read the passage carefully and select the best answer to each question out of the given fouralternatives. Teaching about compassion and empathy in schools can help deal with problems of climate change and environmental degradation,” says Barbara Maas, secretary,
Standing Committee for Environment and Conservation, International Buddhist Confederation (IBC). She was in New Delhi to participate in the IBCs governing
council meeting, December 10-11, 2017. “We started an awareness campaign in the year 2005-2006 with H H The Dalai Lama when we learnt that tiger skins were
being traded in China and Tibet. At that time, I was not a Buddhist; I wrote to the Dalai Lama asking him to say that this is harmful and he wrote back to say, “We
will stop this.” He used very strong words during the Kalachakra in 2006, when he said, If he sees people wearing fur and skins, he doesnt feel like living. This sent
huge shock waves in the Himalayan community. Within six months, in Lhasa, people ripped the fur trim of their tubba, the traditional Tibetan dress. The messenger was ideal and the audience was receptive,” says Maas who is a conservationist. She has studied the battered foxs behavioral ecology in Serengeti,Africa. She heads the endangered species conservation at the Nature and Biodiversity Conservation Union (NABU) International Foundation for Nature, Berlin. “I metSamdhong Rinpoche, The Karmapa, HH the Dalai Lama and Geshe Lhakdor and I thought, if by being a Buddhist, you become like this, I am going for it, “says Maas, who led the IBC initiative for including the Buddhist perspective to the global discourse on climate change by presenting the statement, The Time to Act is Now: aBuddhist Declaration on Climate Change, at COP21 in Paris. “It was for the first time in the history of Buddhism that leaders of different sanghas came together to take a stand on anything! The statement lists a couple ofimportant things: the first is that we amass things that we dont need; there is overpopulation; we need to live with contentment and deal with each other and theenvironment with love and compassion,” elaborates Maas. She is an ardent advocate of a vegan diet because “consuming meat and milk globally contributes more toclimate change than all "transport in the world.” Turning vegetarian or vegan usually requires complete change of perspective before one gives up eating their favorite food. What are the Buddhist ways to bringabout this kind of change at the individual level? “To change our behavior, Buddhism is an ideal vehicle; it made me a more contented person,” says Maas, who grewup in Germany, as a sausage chomping, meat-loving individual. She says, “If I can change, so can anybody”. Why did Ms. Barbara Mass say “If I can change, so can anybody”?

Direction : Two statements I and II are given. These statement may be either independent causes or may be effects of independent causes or a common cause. One of these statements may be the effect of the other statements. Read both the statements and decide which of the following answer choice correctly depicts the relationship between these two statements. Mark answer :

I. The life today is too fast, demanding and full of variety in all aspects which at times leads to stressful situations.
II. Number of suicide cases among teenagers is on increase.

Direction : Two statements I and II are given. These statement may be either independent causes or may be effects of independent causes or a common cause. One of these statements may be the effect of the other statements. Read both the statements and decide which of the following answer choice correctly depicts the relationship between these two statements. Mark answer :

I. The life today is too fast, demanding all full of variety in all aspects which at times leads to stressful situation.
II. Number of suicide cases among teenagers is on increase.

Direction : Two statements I and II are given. These statement may be either independent causes or may be effects of independent causes or a common cause. One of these statements may be the effect of the other statements. Read both the statements and decide which of the following answer choice correctly depicts the relationship between these two statements. Mark answer :

I. Standard of living among the middle class society is constantly going up since part of few years.
II. Indian Economy is observing remarkable growth.

If "÷" denotes "multiplied by", "+" denotes "subtracted from", "–" denotes "added to" and "x" denotes "divided by", then which of the following equation is true?