Question

The following table gives the joint probability distribution between

employment status and college graduation among those either employed or

looking for work (unemployed) in the working-age U.S. Population for 2012.

	Unemployed (Y=0)	Employed (Y=1)	Total
Non-college grads(X=0)	0.045	0.590	0.635
College grads(X=1)	0.015	0.350	0.365
Total	0.060	0.940	1.000

a. Compute E(Y).

b. Compute E(X).

c. Compute Var(Y).

d. Compute Var(X).

e. Compute Cov(X,Y).

f. [Compute Corr(X,Y).

g. The unemployment rate is the fraction of the labor force that is unemployed. Show that the unemployment rate is given by 1 – E(Y).

h. Calculate E(Y|X = 1) and E(Y|X = 0).

i. Calculate the unemployment rate for (i) college graduates and (ii) non-college graduates.

j. A randomly selected member of this population reports being unemployed. What is the probability that this worker is a college graduate? A non-college graduate?

k. Are educational achievement and employment status independent? Use the statistical definition of “independence” of two random variables to justify your answer.

Answer 1