3 Questions for Test 1 - Applied Probability and Statistics I | STAT 400, Exams of Probability and Statistics

Download 3 Questions for Test 1 - Applied Probability and Statistics I | STAT 400 and more Exams Probability and Statistics in PDF only on Docsity! Stat 400 TEST 1 Oct. 20, 2005 J.Millson 1. Let X be a discrete random variable with probability mass function p given by p(0) = 1/6, p(1) = 1/3, p(2) = 1/3, p(3) = 1/6 . (a) Find E(X). (b) Find E(X2). (c) Find V (X). (d) Find F (x), the cumulative distribution function of X. (e) Suppose that we define a new random variable Y by Y = X − 1. Find P (Y = 0). (15 points) 2. Let X be a continuous random variable with the probability density function f(x) = { 2(1 − x), 0 ≤ x ≤ 1, 0, otherwise. (a) Find E(X). (b) Find V(X). (c) Find F (x), the cumulative distribution function of X. (d) Find the median of X. (20 points) 3. A bridge hand consists of 13 cards (out of a 52 card deck) dealt at random. (a) What is the probability that a bridge hand will contain no hearts? (b) What is the probability that a bridge hand will contain only face cards (ie will contain only jacks, queens, kings and aces)? (c) What is the probability that a bridge hand will contain all four aces? (15 points)