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Unformatted text preview: Cumulative Binomial Probabilities • Recall Binomial random variable: 1. an experiment consisting of n indepen dent identical trials, say n = 20; 2. depends on a parameter p , the success probability; 3. counting the number of successes. • Usually denoted by X ∼ Binomial ( n,p ). 1 • How do we describe a discrete random vari able? Use mass function p ( x ) := P ( X = x ) . • For X ∼ Binomial (20 ,. 6), what is its mass function p ( x )? p ( x ) = 20 x (0 . 6) x (0 . 4) 20 x where 20 x = 20! x !(20 x )! and x ! = 1 * 2 * 3 ··· x . 2 Table II on page 785 • Because of the significance of Binomial dis tributions, their mass functions are usually well known and very well tabulated. • Those listed values are cumulative proba bilities, P ( X ≤ k ) = P ( X = 1) + ··· + P ( X = k ) . • Remark: Knowing mass function is equiv alent to knowing cumulative probabilities....
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 Spring '10
 Zhao
 Binomial, Counting, Probability

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