Binomial Distribution Approximated by Gaussian Distribution
Jump to navigation
Jump to search
Theorem
Let $X$ be a discrete random variable which has the binomial distribution $\Binomial n p$.
Then for large $n$ and such that both $n p$ and $n q$ are approximately $5$ or more:
- $\Binomial n p \approx \Gaussian {n p} {n p q}$
where $\Gaussian {n p} {n p q}$ denotes the Gaussian distribution.
Proof
This theorem requires a proof. In particular: Use Central Limit Theorem You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): binomial distribution
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): binomial distribution