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Unformatted text preview: 3.5 Hypergeometric and Negative Binomial Distributions There are N balls in an urn of which M are white. Choose n balls without replacement. Let X=# white balls in the selection . P(X=x)=p(x)= -- n N x n M N x M For x is an integer satisfying max(0, n-N+M) x min(n,M) Example 3.36/ page 117: E(X)=nM/N, V(X)= - -- N M N M n N n N 1 1 Negative Binomial: Perform independent Bernoulli trials. Let X=# of failures until we obtain r successes. P(X=k)=P(r successes, k failures, last trial is a success)= k k p p k k x ) 1 ( 1 1- -- + , E(X)=r(1-p)/p, V(X)= 2 ) 1 ( p p r- In some books, Y= # of trials needed to get rth success is defined to be NB rv. HW assignment: Section 3.5: #69-77 odd 70* 1 3.6 The Poisson Probability Distribution Consider the following occurrence of rare events: (i) Number of accidents takes place (ii) Number of tornadoes in a year (iii) Number of people affected by a disease. Such phenomena, with small probability of occurrence (called rare events), can be described by Poisson distribution....
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- Spring '08