Problem 6: Let A and B be random variables and let

W =A - n B

for some positive number n. (Thinking of long cash commodity and short

futures on that commodity.)

Problem 6: Let A and B be random variables and let W = A n B for some positive number n. (Thinking of long cash commodity and short futures on that commodity.) (a) Find V(W) in terms of variances of A and B , the covariance of A and B, and 11. Your appendix on Random Variables gives you the relevant formulae. (b) Treat V(w) as a function of n. What type of function is this? Describe the graph of this function. Does it have a maximum or minimum point? Explain. dV(W) (c) Using, '1" nd the n that produces the maximum or minimum value of V(W). Be sure to explain using calculus. (d) The Correlation : _ Cov(A,B) GAGE 9,4,3 Using this formula express your values of n -om part c in terms of: PA,B ,0A .03