VCE Together Year 12 Mathematical Methods: Bernoulli Trials and the Binomial Distribution

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# Bernoulli Trials and the Binomial Distribution

Bernoulli Trials and the Binomial Distribution is a part of the VCE Maths Methods topic Probability and Statistics and subtopic 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)

### The Bernoulli Distribution

The following video introduces 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.

### The Binomial Distribution

The following two videos will introduce the binomial probability distribution and how to find unknown parameters.

##### Part 2

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