Chapter 3b - USING THE BINOMIAL CUMULATIVE DISTRIBUTION...

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USING THE BINOMIAL CUMULATIVE DISTRIBUTION FUNCTION TO FIND PROBABILITIES The cumulative distribution function represents P(X < x). The binomial tables present the CDF of the binomial distribution for various values of n, p, and x. Let n =4 and p = .2 Find P(X < 3). Find P(X = 2) Find P(X > 2)
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NEGATIVE BINOMIAL PROBABILITY DISTRIBUTION Conditions: The number (n) of trials is fixed. The number of successes will vary from experiment to experiment. The probability of getting a success, p, is constant throughout the trials. The trials are observed until exactly r successes are obtained (r is a positive integer set by the experimenter). The random variable X is the number of trials needed to obtain the r successes. Negative Binomial Probability Function: For r = 1, 2, 3, … and x = r, r+1, r+2, … 1 ( ) (1 ) 1 r x r x P x p p r - -   = -   -   Binomial vs. Negative Binomial Distribution: Binomial: What is the probability of 2 successes out of 3 trials? Number of trials is fixed but numbers of successes can vary. Negative Binomial: What is the probability that it will take three trials to get two successes? Number of successes is fixed but number of trials to get those successes can vary.
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Mean and Variance of Negative Binomial distribution E(X) = r/p Var(X) = r(1-p)/p 2 Shape of the distribution depends on r and p: All plots shown here with mean of 10
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This note was uploaded on 01/17/2011 for the course STAT 4714 at Virginia Tech.

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Chapter 3b - USING THE BINOMIAL CUMULATIVE DISTRIBUTION...

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