Probability Distributions

Probability Distributions - Summary of Discrete Probability...

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Summary of Discrete Probability Distributions Description Examples p(x) or f(x) μ = E(x) Variance σ 2 Std. Dev. σ Binomial (Discrete) Experiments involving only two outcomes. Example: Flipping a coin and counting number of Heads (X), i.e. successes , in a fixed number of trials (n). On any trial, the probability of success is p and probability of failure (i.e., obtaining a Tail), q = 1-p. When p = q = 0.5, it's called a symmetric binomial distribution. NOTE: When n is large and p is small, binomial distribution can be approximated by Poisson distribution with np = Poisson parameter λ. When n is large, binomial distribution can also be approximated by continuous Normal distribution. n x where q p x n x X P x n x ,.., 2 , 1 , 0 , ) ( = = = - and q = 1- p np Note: Expected number of failures = n - E(X) = n - np = n(1 - p) = nq npq npq Poisson (Discrete) A type of probability distribution that is often useful in describing the number of times an event occurs in a specific period of time or in a specific area or volume. Examples: (i) Number of customer arrivals per minute at a supermarket checkout. (ii) Number of industrial accidents per month at a manufacturing plant. (iii) Number of death claims received per day by an insurance company. 0 ,... 3 , 2 , 1
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Probability Distributions - Summary of Discrete Probability...

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