Lecture8

Lecture8 - Important Distributions Discrete Uniform...

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Important Distributions 10/20/2005

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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 0 < 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

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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. Let T be the number of trials up to and including the first success.

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