EC2303 Foundations for Econometrics Matriculation

Name: EC2303 Foundations for Econometrics Matriculation #: PS2 Tutorial Section (W#): Week 4: Problem Set 2 DUE: Monday 9 September, 12pm • Please hand in to the economics office (AS2 -L6) • Late assignments will not be accepted. • Show your work to get full credit. • Carry through fractions or exact decimals when possible. You can round final answers to two decimal places. 1. (4 pts) X and Y are discrete random variables with the following joint distribution: Value of Y 14 22 32 40 65 2 0.05 0.02 0.10 0.03 0.01 Value of X 5 0.17 0.15 0.05 0.02 0.01 8 0.02 0.03 0.15 0.10 0.09 That is, P(X = 2; Y = 14) = 0:05, and so forth. (a) Calculate the probability distribution, expected value, and variance of X. Calculate the probability distribution, expected value, and variance of Y. (b) Are X and Y independent? Justify your answer. For the next two problems, review the last lecture slides from W4 or see Section 4.7 of the textbook (c) Calculate the probability distribution and mean of Y given X = 8. (d) Let W denote a random variable such that W = 2X + Y . Compute E(W) and V ar(W) 1 EC2303 -Foundations for Econometrics Version: September 3, 2013 2. (3 pts) Suppose that all five-card poker hands (C52 5 ) are equally likely (no jokers). What is the probability of being dealt the following hands? (a) A flush (all five cards are the same suit) (b) 1 pair (a; a; b; c; d -where a, b, c, d are all distinct) (c) Straight (a; a + 1; a + 2; a + 3; a + 4) -that is, 5 consecutive cards such that not all cards are the same suit (that would be a straight flush). Note that an ace can count as the lowest or highest card in a straight -either (ace, two three, four, five) or (ten, jack, queen, king, ace). 3. (2 pts) Suppose people enter a shopping market at the rate of 1 person every 2 minutes. (a) What is the probability that no one enters between 10:15am and 10:20? (b) What is the probability that at least 4 people enter between that same time? Feel free to use a probability table for both..