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== Problem 1: Binomial Proofs == | == Problem 1: Binomial Proofs == | ||
Let <math>X</math> denote a binomial random variable with parameters <math>(N, p)</math>. | Let <math>X</math> denote a binomial random variable with parameters <math>(N, p)</math>. | ||
| + | *(a) Show that <math>Y = N - X</math> is a binomial random variable with parameters <math>(N,1-p)</math> | ||
| + | *(b) What is <math>P\{X</math> is even}? Hint: Use the [http://en.wikipedia.org/wiki/Binomial_theorem binomial theorem] to write an expression for <math>(x + y)^n + (x - y)^n</math> and then set <math>x = 1-p</math>, <math>y = p</math>. | ||
== Problem 2: Locked Doors == | == Problem 2: Locked Doors == | ||
Revision as of 07:58, 18 September 2008
Contents
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 $.
