Statistical Sciences 2141A/B Lecture Notes - Lecture 15: Bernoulli Distribution, Bernoulli Trial, Binomial Distribution

• School: Western University
• Department: Statistical Sciences
• Course: Statistical Sciences 2141A/B
• Professor: Joe Raaymakers

Document Summary

Different kinds of probability distributions are related by certain parameters in them. This makes them a family of probability distributions. The simplest discrete rv is one that can take just two values and can be used to model any process that has only two possible outcomes (e. g. , success or failure, heads or tails, etc. ) Typically the outcomes are labeled 0 and 1 and the rv is defined by the parameter p, 0 p 1, which is the probability the outcome is 1. A bernoulli random variable is any rv whose only possible values are 0 and 1 and it has mean and variance. Consists of a sequence of n bernoulli trials, where n is fixed in advance of the experiment (e. g. , tossing a coin repeatedly) Is conducted such that the trials are independent (i. e. , the outcome of any particular trial does not affect the outcome of any other trial) Has a constant probability of success p for each trial.