A stockbroker recommends three stocks Cisco ATT and Intel to

A stockbroker recommends three stocks (Cisco, AT&T, and Intel) to his clients. If all three of them rise in price over the next year, he gets a bonus of $50,000, if two of them rise, he gets a bonus of $30,000, if one rises, he gets $10,000 and he gets nothing if none of them rise in price. Assume that for any of these stocks, the probability it rises over the next year is 12.

a) Let X be the number of stocks that rise in price. What values can X take on? What is the distribution of X?

b) Let Y be the stockbroker’s bonus. Is Y a random variable? Why or why not?

c) What is the distribution of Y?

d) What is the probability the stockbroker’s bonus is at least $30,000?

Solution

THERE ARE 3 STOCKS IN TOTAL

A) X BE THE STOCKS WHICH INCREASED THERE PRICES AND IT CAN TAKE VALUES FROM

VALUE AND DISTRIBUTION TABLE

0 3C0 *(1/2)^3 = 1/8

1 3C1 *(1/2)^3 = 3/8

2 3C2*(1/2)^3 = 3/8

3 3C3*(1/2)^3 = 1/8

B) LET Y BE THE BONOUS THEREFORE Y IS NOT A RANDOM VARIABLE BECAUSE ITS VALUES WILL DEPEND ON THE VALUES OF X AND HENCE IT IS NOT INDEPENDENT

C) DISTRIBUTION OF Y

0 = 1/8

10,000 = 3/8

30000 = 3/8

50000 = 1/8

D) BONUS IS ATLEAST 30,000 = THIS WILL INCLUDE BOTH 30,000 AND 50,000 = 3/8+1/8 = 4/8 = 1/2