1 / 7

Understanding the Binomial Mean and Variance: Simple Calculations Explained

This article provides a clear explanation of the mean and variance for the Binomial Distribution. If X follows a Binomial distribution B(n, p), the mean is calculated as E(X) = np, while the variance is given by Var(X) = npq, where q = 1 - p. The article explores the reasoning behind these formulas through examples and proofs, making the concepts accessible to learners. Discover the significance of these statistical measures and their applications in probability theory.

jayme-ramirez
Télécharger la présentation

Understanding the Binomial Mean and Variance: Simple Calculations Explained

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. www.making-statistics-vital.co.uk MSV 40: The Binomial Mean and Variance

  2. One of the first things you ask on being shown a new probability distribution is: ‘What’s the mean? And what’s the variance?’ For the Binomial Distribution, there are simple answers. If X ~ B(n, p), then the mean of X = E(X) = np. If X ~ B(n, p), then the variance of X = Var(X) = npq, where q = 1 - p.

  3. Being a good mathematician, you will ask, ‘Can I prove these things?’ E(X) = np makes sense. If you roll a normal dice 60 times, then you would expect on average the number of sixes rolled to be 10 = 60 x 1/6. The formula for the variance is harder to see.

  4. Let’s try to prove these results for a special case. Suppose X ~ B(3, p) for some p. Can you prove that E(X) = 3p and Var (X) = 3p(1 - p) ? Try!

  5. If X ~ B(3, p) then we have = 3p.

  6. Var(X) = E(X2) - (E(X))2. So Var(X) = E(X2) - (E(X))2 = 6p2 + 3p – (3p)2 = 3p – 3p2 = 3p(1-p).

  7. With thanks to pixabay.com www.making-statistics-vital.co.uk is written by Jonny Griffiths hello@jonny-griffiths.net

More Related