18. Suppose all the stocks in Bob’s portfolio double in price.
a. What happens to the mean of Bob’s stocks?
Want E(2X) = 2x20 = $40
b. What happens to the variance?
Want V(2X) = 4x25 = 100
19. Suppose all of Sue’s stocks each increase $10.00 in price.
ab.
What happens to the mean and variance of her stock prices?
E(Y+10)=30+10=$40; V(Y+10)=36
20. Assume Bob and Sue’s stocks are independent.
a. What is the mean and standard deviation of their combined stock prices?
E(X+Y)=20+30=$50
V(X+Y) = 26+36=61 by independence; SD(X+Y)=square root of 61=$7.8
b. What is the mean and standard deviation of the difference in their stock prices?
E(XY)=2030=$10
V(XY)=26+36=61 by independence; SD(XY)=$7.8
21. Assume Bob and Sue’s stocks have correlation 0.4.
a. What is the mean and standard deviation of their combined stock prices?
E(X+Y)=$50 as before
V(X+Y)=25 + 36 + 2(.4)(5)(6)=85; SD(X+Y)=square root of 85 = 9.22
b. What is the mean and standard deviation of the difference in their stock prices?
E(XY)=$10 as before
V(XY)=25 + 36  2(.4)(5)(6)=37; SD(XY)=square root of 37=6.08
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 Fall '11
 Johnson
 Statistics, Standard Deviation, Probability theory, Brandt Data Solutions

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