Homework4 ECE302Fall2008sanghavi - Rhea

Instructions

Homework 4 can be downloaded here on the ECE 302 course website.

Problem 1: Binomial Proofs

Let $ X $ denote a binomial random variable with parameters $ (N, p) $.

• (a) Show that $ Y = N - X $ is a binomial random variable with parameters $ (N,1-p) $
• (b) What is $ P\{X $ is even}? Hint: Use the binomial theorem to write an expression for $ (x + y)^n + (x - y)^n $ and then set $ x = 1-p $, $ y = p $.

Problem 2: Locked Doors

Problem 3: It Pays to Study

Problem 4: No Deal