Suppose random variables X and Y are independent and that X has expected value 5 and variance 4 and Y has expected value 7 and variance 9. Compute the following:

a) VAR(X-Y) = ? and VAR(X-3) = ?

b)Suppose, furthermore you know that X and Y are normal random variables. Describe the probability model for X+Y . (You need to give its name, if possible, and

clearly state the values of its parameters.)

c) If you were told that Cov(X,Y) = 3 , and that X and Y are not independent, what would Var(X-Y) be?

d) Consider the below information given in terms Histogram of class relative frequencies about a data set. On the space provided on the right, draw the corresponding relative

Frequency histogram.

Class Relative Frequency (%) 0-5 10 5- 10 20 10 - 15 20 15 - 20 30 20 - 25 20