Applied Econometrics

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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

  1. The following table gives the joint probability distribution between employment status and collegegraduationamongthoseeitheremployedorlookingforworkintheworkingageUSpopulation for 2008.

 

  Unemployed

 

(Y= 0)

Employed

 

(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

 

  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(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
  2. 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)
  3. 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)?
  4. e) Are educational achievement and employment status independent?Explain

 

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

that and s 2 =1

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