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104 Chapter 2 Review of Probability

c. What is the standard deviation of C?
d. Convert the answers to (a) through (c) from U.S. dollars ($) to

euros (:).
2.8 The random variable Y has a mean of 4 and a variance of 1/9. Let Z =

3(Y - 4). Find the mean and the variance of Z.
2.9 X and Y are discrete random variables with the following joint distribution:

Value of Y
2 4 6 8 10
0.04 0.09 0.03 0.12 0.01
Value of X 3 0.10 0.06 0.15 0.03 0.02
6 0.13 0.11 0.04 0.06 0.01

9

That is, Pr(X = 3, Y = 2) = 0.04, and so forth.

a. Calculate the probability distribution, mean, and variance of Y.
b. Calculate the probability distribution, mean, and variance of Y given

X = 6.
c. Calculate the covariance and correlation between X and Y.

2.10 Compute the following probabilities:

a. If Y is distributed N(4, 9), find Pr(Y … 5).
b. If Y is distributed N(5, 16), find Pr(Y 7 2).
c. If Y is distributed N(1, 4), find Pr(2 … Y … 5).
d. If Y is distributed N(2, 1), find Pr(1 … Y … 4).

2.11 Compute the following probabilities:

a. If Y is distributed x23, find Pr(Y … 6.25).
b. If Y is distributed x28, find Pr(Y … 15.51).
c. If Y is distributed F8,∞, find Pr(Y … 1.94).
d. Why are the answers to (b) and (c) the same?
e. If Y is distributed x12, find Pr(Y … 0.5). (Hint: Use the definition of

the x12 distribution.)

2.12 Compute the following probabilities:

a. If Y is distributed t12, find Pr(Y … 1.36).