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

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Presentation on theme: "The Binomial Distribution: Mean and Variance © Christine Crisp “Teach A Level Maths” Statistics 1."— Presentation transcript:

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

2 The Binomial Distribution – Mean and Variance "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages" Statistics 1 AQA MEI/OCR OCR

3 The Binomial Distribution – Mean and Variance 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.

4 The Binomial Distribution – Mean and Variance Suppose. The probability distribution is 3210x Can you find the mean using the formula for any discrete probability distribution? mean,  = If you’ve forgotten how to calculate the mean, the results written in a table may remind you: Can you spot the link to the parameters of the distribution ( n = 3 and p = 0·4 )?

5 The Binomial Distribution – Mean and Variance mean,  = 3210x 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: ANS: so, Suppose. The probability distribution is

6 The Binomial Distribution – Mean and Variance 3210x The formula for the variance of any discrete probability distribution is variance Now for the variance: The link with the parameters isn’t so easy to spot this time but it’s easy to remember. It is 9410x2x2

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

8 The Binomial Distribution – Mean and Variance Exercise Solutions: 1. Find the mean and variance of the random variable X where (a) (b) (c) (d) (a) mean variance (b) mean variance

9 The Binomial Distribution – Mean and Variance Exercise Solutions: 1. Find the mean and variance of the random variable X where (a) (b) (c) (d) (c) mean variance (d) mean variance

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

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


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