Two electronic traded funds (ETF's) which we call ETF A and ETF B have the following distribution for their annual rate of return. Let X and Y be the rate of returns for the ETFs. a) Assuming the ETF return probabilities are independent, find the joint probability distribution f(x, y). b) If $40,000 is invested in ETF X, what is the probability of losing money? What if it is all $40,000 is invested in ETF Y? Which investment is safer? Explain. c) Find the 4 by 4 payoff matrix when $10,000 is invested in ETF X and $30,000 is invested in ETF Y. d) What is the probability of a loss when $10,000 is invested in ETF X and $30,000 is invested in ETF Y