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Statistics Distribution Binomial Distribution Chapter 4: Summary of Discrete Probability Distributions Summary Formulas A binomial experiment satisfies the following conditions: x= 1. The binomial experiment is repeated for a fixed number (n) of independent trials. 2. There are only two possible outcomes—a success or a failure. 3. The probability of a success remains constant for each trial. 4. The random variable x counts the number of successful trails out of the n trials. The parameters of a binomial distributions are Geometric Distribution A geometric distribution is a discrete probability distribution of a random variable x that satisfies the following conditions: 1. A trial is repeated until a success occurs. 2. The repeated trials are independent of each other. 3. The probability of success p is constant for each trial. 4. The random variable x represents the number of the trial in which the first success occurs. Calculator Steps Use binompdf p= q= Use binomcdf q= The probability of exactly x successes in n trials is: x= Use 1-binomcdf Use geometpdf p= q= Use geometcdf q= The parameters of a geometric distribution are Poisson Distribution The Poisson distribution is a discrete probability distribution of a random variable x that satisfies the following conditions: 1. The experiment consists of counting the number of times an event, x, occurs over a specified interval of time. 2. The probability of each event occurring is the same for each interval. 3. The number of occurrences in one interval is independent of occurrences in other intervals. The parameters of a Poisson distribution are 4 The probability that the first success occurs on trial number x is: Use 1-geometcdf x= Use poissonpdf = Use poissoncdf The probability of exactly x occurrences in an interval is: Use 1-poissoncdf