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 | |
| 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 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
- 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 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(Y-1). Show that m Z =0
|
that and s 2 =1