Lesson 7 Useful Probability Distributions

Lesson 7 Useful Probability Distributions - Some Discrete...

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Some Discrete Probability Distribution I. Discrete Uniform Distribution - Simplest of all discrete probability distributions. - random variable assumes each of its values with equal probability. Definition: If the random variable X assumes the values x1, x2, x3,…,xk, with equal probabilities, then the discrete uniform distribution is given by where x = x1, x2, x3, …, xk. The mean and the variance of the discrete uniform distribution f(x;k) are Note: The histogram of this distribution is a set of f ( x ; k ) = 1 k μ= 1 k x i σ 2 = i = 1 k 1 k x i ( 29 2 i = 1 k

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Examples 1. An employee is selected from a staff of 10 to supervise a certain project by selecting a tag at random from a box containing 10 tags numbered 1 to 10. Find the formula for the probability distribution of X representing the umber on the tag that is drawn. What is the probability that the number drawn is less than 4? 1. A box contains 12 similarly shaped colored balls numbered 1 - 12. Let the random variable X represent the number on the ball that is drawn. What is th probability distribution of X? What is its mean and variance?
Binomial Distribution - Involves the discrete random variable X representing the number of successes in n Bernoulli trials/processes. -

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Lesson 7 Useful Probability Distributions - Some Discrete...

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