STAT 3450 Lecture Notes - Lecture 9: Bernoulli Distribution, Bernoulli Trial, Binomial Distribution
6 Mar 2017
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Probability distributions (probability mass functions or probability density functions) for random variables can be derived from simple experiments. Simple examples: flipping coins, rolling dice, dealing cards, etc. In many cases, scientific knowledge about a problem at hand suggests the use of a particular distribution as a model for a random variable. A bernoulli trial is an experiment that can result in one of two possible outcomes. One outcome is labeled success and the other outcome is labeled failure . X is an rv with only two outcomes, represented numerically as 1 (success) and 0 (failure). If the focus is on the outcome of heads then heads represent success and tails represent failure. The probability of success, p, is the parameter of the bernoulli distribution and the probability of failure is 1 p in general. (in case of a fair coin p = 1 p = ) Mean, variance, and standard deviation of a bernoulli random variable:
