Econ 1150
Applied Econometrics
Mini-Exam 1
1. The random variable Y is the number of new followers that Taylor Swift’s Instagram account on any given day. Assume that Y is continuous and follows a normal distribution N(10000, 4202
). Find the following probabilities.
(a) P r(Y < 10357)
(b) Pr({9370 < Y < 9580} or {10420 < Y < 10840})
2. Information on new restaurants in Pittsburgh was collected. Specifically, the researcher checked whether the restaurants offered vegan items on the menu (V = 1) or not (V = 0) and whether they stayed in business for at least a year (B = 1) or not (B = 0). The joint distribution of these variables are given by the following table:
(a) What is the proportion of restaurants that offer vegan items on their menu?
(b) Given that a restaurant stayed in business for at least a year, what is the probability that this restaurant offered vegan items on its menu?
(c) Are these variables (V and B) independent? (Hint: Use the marginal probabilities.)
3. X and Z are two random variables. We have P(Z = 1) = 0.7 and P(Z = 2) = 0.3. We also know E(X|Z = 1) = 9 and E(X|Z = 2) = 0. Calculate E(X).