# The Binomial Distribution: Mean and Variance

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The Binomial Distribution: Mean and Variance
“Teach A Level Maths” Statistics 1 The Binomial Distribution: Mean and Variance © Christine Crisp

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There are very simple formulae that we can use to find the mean and variance of a Binomial Distribution. I’ll illustrate the formulae with an example.

3 2 1 x Suppose . The probability distribution is
Can you find the mean using the formula for any discrete probability distribution? If you’ve forgotten how to calculate the mean, the results written in a table may remind you: 3 2 1 x mean, m = Can you spot the link to the parameters of the distribution ( n = 3 and p = 0·4 )?

3 2 1 x Suppose . The probability distribution is
Can you find the mean using the formula for any discrete probability distribution? If you’ve forgotten how to calculate the mean, the results written in a table may remind you: 3 2 1 x mean, m = ANS: so,

x2 1 4 9 3 2 1 x Now for the variance:
1 4 9 3 2 1 x The formula for the variance of any discrete probability distribution is The link with the parameters isn’t so easy to spot this time but it’s easy to remember. It is variance

e.g.1 Find the mean and variance of the random variable X where
Solution: mean, variance variance SUMMARY The mean of a Binomial Distribution is given by mean, The variance is given by variance

Exercise 1. Find the mean and variance of the random variable X where
Solutions: (a) mean variance mean (b) variance

Exercise 1. Find the mean and variance of the random variable X where
Solutions: (c) mean variance mean (d) variance

The following slide contains repeats of information on earlier slides, shown without colour, so that it can be printed and photocopied.

variance SUMMARY mean, The variance is given by The mean of a Binomial Distribution is given by Solution: e.g.1 Find the mean and variance of the random variable X where