Question

India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too high to be sustainable. A demographer assumes the following probability distribution for the household size in India.

Household Size	Probability
1	0.05
2	0.09
3	0.12
4	0.24
5	0.25
6	0.12
7	0.07
8	0.06

Compute the mean of the household size in India?

Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading.

Grade	Numerical Score	Probability
A	4	0.10
B	3	0.30
C	2	0.40
D	1	0.10
F	0	0.10

Compute the variance of the numerical score.

You have $400,000 invested in a well-diversified portfolio. You inherit a house that is presently worth $200,000. Consider the summary measures in the following table:

Investment	Expected Return (in %)	Standard Deviation (in %)
Old portfolio	6	16
House	8	20

The correlation coefficient between your portfolio and the house is 0.38.

What is the standard deviation of new portfolio which includes old portfolio and house?

	a.	16.55%
	b.	13.25%
	c.	15.32%
	d.	14.56%

Questions below are separate

1. If E(X) = 10 and E(Y) = 20, Var(X) = 3, Var(Y) = 5 and Cov(X, Y) = 10, then

what is the var(Z) where Z = 3X+2Y?

2. If E(X) = 10 and E(Y) = 20, Var(X) = 3, Var(Y) = 5 and Cov(X, Y) = 10, then

what is the mean of Z where Z = 3X+2Y?

Note that mean of Z = E(Z).

3. If correlation coefficient =0.3 and Var(X) =25 and Var(Y) = 16, then what is Cov(X, Y)?

Answer 1