Temple University

Department of Economics

Economics 615 Econometrics I

Descriptive Statistics, Probability and Random Variables

1. A biologist notes that the probability an insect of a particular breed is red is .60. The probability it is winged is .50. She also notes that the probability it is red, winged or both is .80.
a. What is the probability that a randomly selected insect is both red and winged?
b. What is the probability that it is red, given that it is winged?
c. Are the events 'color' and 'winged' statistically independent?

2. Monty Hall plays a game with his TV show participants to teach a valuable lesson in probability. There are three curtains denoted A, B, and C on stage with a prize behind each. One of the prizes is quite valuable, the other two have only nominal value. The participant picks a curtain, although at this point it remains closed. Monty then opens one of the remaining curtains to reveal a prize of nominal value. The participant may now choose between the two remaining closed curtains; i.e., stick with her original choice or switch. What strategy would you recommend? Explain.

3. A sample of 10 major symphony conductors has been selected. The number of years that each has spent as a conductor is: 10, 7, 32, 17, 5, 23, 19, 14, 8, 2. Calculate the sample mean, sample median, sample variance and sample standard deviation.

4.  The discrete random variable Y has the probability mass function

Show that the mean of the random variable Y does not exist.

5. Below is the joint distribution for the random variables X and Y.

a. What is the marginal distribution of X.
b. What is the distribution of X given Y=2.
c. Find E(x)
d. Find Var(x)
e. Find E(X|Y=2)
f. Find Var(x|Y=2)