L09_S10R - AMS 311, Spring Semester 2010 Lecture 9 4.6. The...

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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{ ) ( =...
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L09_S10R - AMS 311, Spring Semester 2010 Lecture 9 4.6. The...

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