This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: AMS 311, Spring Semester 2010 Lecture 9 4.6. The Bernoulli and Binomial Random Variables Definition A random variable is called Bernoulli with parameter p if its probability mass function is p p = 1 ) ( and p p = ) 1 ( and 0 otherwise. When X is a Bernoulli random variable with parameter p , what is E(X) ? What is var( X )? Binomial Distribution B(n,p) Counts number of successes in n total trials. The trials are independent and homogeneous. Let X be a binomially distributed random variable for n trials and probability of success p . Probability mass function: n x p p x n x X x p x n x , , 2 , 1 , , ) 1 ( } Pr{ ) ( = = = = . np X E = ) ( ; ) 1 ( ) var( p np X = . Consider a sequence of independent Bernoulli random variables n X X X , , , 2 1 where n is a fixed integer. We seek to describe the random variable ∑ = = n i i n X S 1 . Then the probability function for S n is given by n x p p x n x S x p x n x n , , 2 , 1 , , ) 1 ( } Pr{ ) ( =...
View
Full
Document
This note was uploaded on 04/13/2010 for the course AMS 311 taught by Professor Tucker,a during the Spring '08 term at SUNY Stony Brook.
 Spring '08
 Tucker,A

Click to edit the document details