5 Let Xi be the price (in dollars) of stock i one year from now. X1 is N(15, 100) and X2 is N(20, 2025). Today I buy three shares of stock 1 for $12/share and two shares of stock 2 for $17/share. Assume that X1 and X2 are independent random variables.

a Find the mean and variance of the value of my stocks one year from now.

b What is the probability that one year from now I will have earned at least a 30% return on my investment?

c If X1 and X2 were not independent, why would it be difficult to answer parts

(a) and (b)?