Exam 5: Several Useful Discrete Distributions

A hypergeometric probability distribution shows the probabilities associated with possible values of a discrete random variable when these values are generated by sampling with replacement and the probability of success, therefore, changes from one trial to the next.

The number of traffic accidents per day on a certain section of highway is thought to be Poisson distributed with a mean equal 2.19. Based on this, how many traffic accidents should be expected during a week long period?

A jug contains 5 black marbles and 5 white marbles well mixed. A marble is removed and its color noted. A second marble is removed, without replacing the first marble, and its color is also noted. If x is the total number of black marbles in the two draws, then x has a binomial distribution.

The Poisson random variable is:

Let x be a hypergeometric random variable with N = 12, n = 4, and M = 3. Calculate p(0). ______________ Calculate p(1). ______________ Calculate p(2). ______________ Calculate p(3). ______________ Calculate the mean. ______________ Calculate the variance. ______________ What proportion of the population of measurements fall into the interval ? ______________ Into the interval ? ______________ Do these results agree with those given by Tchebysheff's Theorem? ______________

If x is a binomial random variable with n = 20, and p = 0.5, then P(x = 20) = 1.0.

The hypergeometric random variable is the number of successes achieved when a random sample of size n is drawn with replacement from a population of size N within which M units have the characteristic that denotes success.

Which of the following is an example of a binomial experiment?

The number of traffic accidents per day on a certain section of highway is thought to be Poisson distributed with a mean equal 2.19. Then the probability of no accidents on this section of highway during one day period is approximately: