The following table gives the joint probability distribution between employment status and college graduation among those either employed or looking for work in the working age US population for 2008.

1. The following table gives the joint probability distribution between employment status and college graduation among those either employed or looking for work in the working age US population for 2008.

Unemployed Employed (Y = 0) (Y = 1) Total Non-college grads (X = 0) 0.037 0.622 0.659 College (X = 1) 0.009 0.332 0.341 Total 0.046 0.954 1

a) Using the definition of the expected value, show that the expected value of a binary random variable equals probability of the outcome 1. In other words, suppose you have a random variable that takes on either a value of 1 (called “outcome 1” in the problem set) with probability p or a value of 0 with probability (1-p)). The question asks you to show, using the formula for expected value which you learned in class, that the expected value of this variable equals p

 b) What are the marginal distributions of X and Y? Using a) compute E(Y) and E(X).

c) Calculate E(Y|X = 1 ) and E(Y|X = 0 )

d) Calculate the unemployment rate (probability to be unemployed) for college graduates and noncollege graduates. In other words, suppose you know that someone is a college graduate. What is the probability that she will be unemployed (i.e., conditional probability)?

e) Are educational achievement and employment status independent? Explain.

2. The random variable Y has a mean of 1 and variance of 4. Let Z = ½(Y-1). Show that ? Z ? 0 that and ? Z2 ? 1 . 1