1. Find the mean. and the varial)ce of Y = x, -2X2 + 3X3, where X., X 2 , X 3 are observations of a random sample from a chi-square distribution with 6 degrees of freedom.
2. Let X and Y be random variables such that var (X) = 4, var ( Y) = 2, and var (X + 2Y) = 15. Determine the correlation coefficient of X and Y.
3. Let X and Y be random variables with means µ1 ,µ2 ; variances of , ; and correlation coefficient p. Show that the correlation coefficient of W = ax + b, a > 0, and Z = c Y + d, c > 0, is p.