Assignment # 2
Problem 1. Show that
(i) E(X) = 0 (1 F (x)dx, if X is a continuous r.v. with distribution function F (.).
(ii) E(X) = P (X k), if X is a discrete r.v. .
Problem 2. Suppose that a communication network transmits binary di
Department of Mathematics and Statistics
University of Southern Maine
96 Falmouth Street
Portland, ME 04104-9300
June 29, 2011
1 What is Operations Research ?
2 Review of P
Assignment # 1
Problem 1. Given a r.v. X such that
P (X = j) = (1 )j ,
0 < < 1; 0 j < .
(i) Calculate P (X k).
(ii) Calculate E(X), and show that E(X) is convex and increasing in .
(iii) Calculate P (X = k|X > 0).
(iv) Calculate E(X|X >