MAT 316 Lecture Notes - Lecture 1: Generating Function, Bernoulli Trial, Hypergeometric Distribution
Document Summary
Situation: you are performing a set number n of trials, the trials are bernoulli trials, the trials are all independent, p(success) = p remains constant for each trial. X = the number of successes in the n trials. Note: this is probably the way you saw this presented in sta 215. The same thing can be written in one sentence: you are performing n independent bernoulli trials, each having. X ~ bi( , ) where the can contain any positive integer, and the can contain any real number between 0 and 1. Thinking of it like this will help you to not depend on the notation. It will also be very helpful to you when we start summing sums to find expected values, as you will see shortly. Note: the independence assumption here is very important. The only way the trials can be independent is if the population size is. 1 infinite or if sampling is done with replacement.
