STAT 213 Lecture Notes - Lecture 30: Negative Binomial Distribution, Binomial Distribution, Hypergeometric Distribution

• School: University of Calgary
• Department: Statistics
• Course: STAT 213
• Professor: Anatoliy Swishchuk

Document Summary

1. 2 de nition of the geometric probability distribu- tion. Ek = {f f ff (and so k 1. S} f irst on) on f irst trial; on f irst, success success on second trial; on the third trial; success on the kth trial; De nition (geometric probability distribution): a random vari- able y is said to have a geometric probability distribution with success probability p if and only if p(y) = qy 1p, y = 1, 2, , The geometric probability distribution is often used to model distribu- tions of lengths of waiting times. Suppose that the probability of engine malfunction during any 1-hour period is p = 0. 02. Let y -number of 1-hour intervales until the rst malfunction. P (angine survive 3 hours) = p (y 3) = p(y). P (angine y=1 p(y)+& y=3 p(y) = 1, and& y=3 p(y) = survive 3 hours) = p (y 3) =& y=3 p(y) = 1 &2.