If 1. If for >0 the energy of a pdf is E(x)=r, find the variance. (A) 1 (B) 2 (C) 1/2 (D) Undefined (E) 0

Given pdf f (x) = 1.5x2  for −1< x < 1. Determine variance of X.

Suppose X and Y are two independent variables with variance 1. Let Z = X+bY where b > 0. If Cor(Z, Y ) = 1/2, what is the value of b?

For every ?, ? > 0. 1. Derive the variance of ?.

Suppose that index model for Stocks A and B is estimated from excess returns with the following results : Ra 0.04 +0.6Rm+ea , Rb = - 0.04 + 1.3Rm + eb Risk on the market is 30% , R-squared of A is 30%R - squared of B is 40% , security A residual variance is

If E(X) = 2 and standard deviation of X is 3, what is E(X2)?

2) Let G and H be two independent unbiased estimators of θ. Assume that the variance of G is two times the variance of H. Find the constants a and b so that aG + bH is an unbiased estimator with the smallest possible variance for such a linear combination.

I am not sure how to get the variance for this problem. The answer is 0.703 yr^2. Can someone show me which formula and how they got the answer? Thx

Suppose you have a sample of size n for variables X and Y. The sample covariance of X and Y is  Cov(X,Y) = 1,000, the sample standard deviation for X is Sx=20 and the sample standard deviation for Y is  SY=75.  What is the sample correlation coefficient, r?

If X is a random variable with expectation µ and variance cµ2 , where c is a constant. Find a variance stabilizing transformation of X.