STAB22H3 Chapter Notes - Chapter 5: Bernoulli Trial, Binomial Distribution, Probability Distribution

• School: UTSC
• Department: Statistics
• Course: STAB22H3
• Professor: Caren Hasler

Document Summary

Note: this excludes chapter 5. 2: pascal"s triangle, binomial theorem, and multinomial expansions. , where x is the number of times the preferred outcome occurs, and p(x) is the probability of that outcome (as in the above function and graph) Prerequisites: trials are independent and identical, trials only have 2 outcomes: success and failure: Bernoulli trials: the number of trials (n), along with probabilities of success (p) and failure (q), stay constant p( x)=(n, p x qn x. Illustration 1: chan prefers them like this: theorem: the expectation of the number of successes in a binomial distribution is. The number of expected failures before the first success is obtained p( x)=(x 1. Negative binomial distribution: we"re now interested in finding the rth success on the xth trial. r 1) pr q x r where x is a random variable and we want the rth success. Where r is the trial number: so the 5th success is expected on.