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)?