# 3.5-3.6 - 3.5 Hypergeometric and Negative Binomial...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

{[ snackBarMessage ]}

### Page1 / 8

3.5-3.6 - 3.5 Hypergeometric and Negative Binomial...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online