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 population...

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 population of country A.

a. Compute E(Y).
b. The unemployment rate is a fraction of the labor force that is unemployed. Show that the unemployment rate is given by 1 − E(Y).
c. Calculate E(Y l X = 1) and E(Y l 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 unemployed.
What is the probability that this worker is a (i) college graduate,
(ii) non–graduate?
f. Are educational achievement and employment status independent?
Explain.

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