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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 ( ω ) is defined to be 1 /n for all ω ∈ 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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This note was uploaded on 07/16/2010 for the course MATH 20 taught by Professor Ionescu during the Fall '05 term at Dartmouth.
 Fall '05
 Ionescu
 Probability

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