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Exercises 103

c. Suppose that p = 0.3. Compute the mean, variance, skewness, and
kurtosis of X. (Hint: You might find it helpful to use the formulas
given in Exercise 2.21.)

2.5 In July, Fairtown’s daily maximum temperature has a mean of 65°F and
a standard deviation of 5°F. What are the mean, standard deviation, and
variance in °C?

2.6 The following table gives the joint probability distribution between employ-
ment status and college graduation among those either employed or looking
for work (unemployed) in the working-age population of country A.

Unemployed Employed Total
(Y 0) (Y 1) 0.751
Non–college grads (X = 0) 0.078 0.249
College grads (X = 1) 0.042 0.673 1.000
Total 0.12 0.207
0.88

a. Compute E(Y).

b. The unemployment rate is a fraction of the labor force that is unem-
ployed. Show that the unemployment rate is given by 1 − E(Y).

c. Calculate E(Y ͉ X = 1) and E(Y ͉ X = 0).
d. Calculate the unemployment rate for (i) college graduates and

(ii) non–graduates.

e. A randomly selected member of this population reports being unem-
ployed. What is the probability that this worker is a (i) college graduate,
(ii) non–graduate?

f. Are educational achievement and employment status independent?
Explain.

2.7 In a given population of two-earning male-female couples, male earn-
ings have a mean of $50,000 per year and a standard deviation of $15,000.
Female earnings have a mean of $48,000 per year and a standard devia-
tion of $13,000. The correlation between male and female earnings for a
couple is 0.90. Let C denote the combined earnings for a randomly selected
couple.

a. What is the mean of C?

b. What is the covariance between male and female earnings?