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 September 2017.

a. Compute \(E(Y)\).

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

c. Calculate \(E(Y \mid X=1)\) and \(E(Y \mid X=0)\).

d. Calculate the unemployment rate for (i) college graduates and (ii) noncollege graduates.

e. 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?

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

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Joint Distribution of Employment Status and College Graduation in the U.S. Population Aged 25 and Older, September 2017 Unemployed Employed (Y= 0) (Y=1) Total Non-college grads (X = 0) 0.026 0.576 0.602 College grads (X = 1) 0.009 0.389 0.398 Total 0.035 0.965 1.000