519 Qualifying Exam August 2013
Each problem is worth 20 points. Answers should be in a reasonably simple form.
1. An urn contains 5 balls numbered 1, 2, 3, 4, 5. The balls are identical, aside from the
numbering. Draw two balls from the urn at random, re
MA 51900 PROBABILITY QUALIFYING EXAMINATION
Each question is worth 10 points, so the entire exam consists of 50 points.
1. Three points are chosen independently and uniformly inside the unit square in the
plane. Find the expected
Math 519 Prof. Davis
(Problems 1 and 6 are twelve points each. The others are 19 points
1. Toss a coin with probability p of heads repeatedly. Let X, Y, Z , and W be the
tosses on which the rst, second, third an
August 2011 Prof. Sellke
1. (10 points) Suppose X is N (0, 1) (i.e., standard normal) and Y | X = x is N (x + 1, 1).
(a) (3 points) Find the marginal distribution of Y .
(b) (4 points) Find the correlation between X and Y.
PROBABILITY QUALIFYING EXAMINATION
1. A particle performing a three dimensional random walk starts at time n = 0 at the origin (0, 0, 0).
At each subsequent time n = 1, 2, 3, . . ., the particle moves exactly 1 unit in one direction: either