The money (in thousands of dollars) made from investing in stocks "Ystock" and "Zstock" are mod- eled as the random variables Y and Z. respectively. Assume Y and Z are independent with respective probability density functions fy (y) and 12(z) as shown below:

(a) You want to make as much money as possible, of course. Which stock would you buy?

(b) Suppose you have forgotten your ECE 314, so you decide to flip a coin to decide which stock to buy. What is the probability that you make more than S400?

(c) You decide to rely on some vague idea of the "law of averages", and thus buy 20 Independent

stocks, each of which have the probability density function fy(y). What is the probability that you make more than $400 at least half of the time 10 times)?

4 3+ 2- fy (y) --- N- also+ fi 4- 3+ 2- fz(z) --- 1-4 2460+