Homework 1
Use STATA to find probability distribution /definition of the expected value, marginal distributions
xxxx: Remember use STATA to calculate the problem
SW Chapter 2
 The following table gives the joint probability distribution between employment status and collegegraduationamongthoseeitheremployedorlookingforworkintheworkingageUSpopulation for 2008.
Unemployed
(Y= 0)  Employed
(Y= 1) 
Total  
Noncollege 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 one i the ra value of 1(called”outcome 1″in the problems et ) with probability pora value of 0 with probability(1p)).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(YX=1)and E(YX =0)
 d) Calculate the unemployment rate(probability to be unemployed) for college graduates and non college 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
 The random variable Y has a mean of 1 and variance of 4. Let Z=½(Y1). Show that m Z =0

that and s 2 =1