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 2008.

Joint Distribution of Employment Status and College Graduation in the U.S. Population Aged 25 and Greater, 2008
Unemployed (Y=0) Employed (Y=1) Total
Non-college grads (X=0) 0.037 0.622 0.659
College grads (X=1) 0.009 0.332 0.341
Total 0.046 0.954 1

a. Compute E(Y)
b. The unemployment rate is the fraction of the labor force that is employed. 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-college graduates.
e. A randomly selected member of this population reports being unemployed. What is the probability that this worker is a college graduate?
f. Are educational achievement and employment status independent? Explain.