This is part of the HSC Mathematics Extension 1 course under the topic: The Binomial Distribution.
Let’s start by understanding the Bernoulli distribution.
The Bernoulli distribution is a discrete distribution, which means it’s outcomes have only one of two values: 0 or 1. Typically 1 is the success, and 0 is the failure.
If p is the probability of success.
- The expectation of the distribution is p
- The variance is p(1-p)
All about the Bernoulli distribution
Now we know a little bit about the distribution, let’s use a Bernoulli random variable as a model for two-outcome situations.
Here we will also understand the concepts of Bernoulli trials and the concept of a binomial random variable as the number of ‘successes’ in independent Bernoulli trials, with the same probability of success in each trial.
Frequency from the Bernoulli distribution
Let’s learn to calculate the expected frequencies of the various possible outcomes from a series of Bernoulli trials.