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Unformatted text preview: Important Distributions 10/20/2005 Discrete Uniform Distribution All outcomes of an experiment are equally likely. If X is a random variable which represents the outcome of an ex periment of this type, then we say that X is uniformly distributed. If the sample space S is of size n , where < n < , then the distribution function m ( ) is defined to be 1 /n for all S . 1 Binomial Distribution The distribution of the random variable which counts the number of heads which occur when a coin is tossed n times, assuming that on any one toss, the probability that a head occurs is p . The distribution function is given by the formula b ( n, p, k ) = n k p k q n k , where q = 1 p . 2 Exercise A die is rolled until the first time T that a six turns up. 1. What is the probability distribution for T ? 2. Find P ( T > 3) . 3. Find P ( T > 6  T > 3) . 3 Geometric Distribution Consider a Bernoulli trials process continued for an infinite number of trials; for example, a coin tossed an infinite sequence of times....
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 Fall '05
 Ionescu
 Probability

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