AP Statistics Curriculum 2007 Limits Poisson2Bin

From Socr

Revision as of 16:58, 28 June 2010 by Jenny (Talk | contribs)
(diff) ← Older revision | Current revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Contents

General Advance-Placement (AP) Statistics Curriculum - Poisson as Approximation to Binomial Distribution

Poisson as Approximation to Binomial Distribution

The complete details of the Poisson Distribution as a limiting case of the Binomial Distribution are contained here.

np < 10
n \geq 20 and p \leq 0.05.

Examples

The Binomial distribution can be approximated well by Poisson when n is large and p is small with np < 10, as stated above. This is true because  \lim_{n \rightarrow \infty} 
{n \choose x} p^x(1-p)^{n-x}=\frac{\lambda^x e^{-\lambda}}{x!} , where λ = np. Here is an example. Suppose  2\% of a certain population have Type AB blood. Suppose 60 people from this population are randomly selected. The number of people X among the 60 that have Type AB blood follows the Binomial distribution with n = 60,p = 0.02. The figure below represents the distribution of X. This figure also shows P(X = 0).

  • Note: This distribution can be approximated well with Poisson with λ = np = 60(0.02) = 1.2. The figure below is approximately the same as the figure above (the width of the bars is not important here. The height of each bar represents the probability for each value of X which is about the same for both distributions).

Problems




Translate this page:

(default)

Deutsch

Español

Français

Italiano

Português

日本語

България

الامارات العربية المتحدة

Suomi

इस भाषा में

Norge

한국어

中文

繁体中文

Русский

Nederlands

Ελληνικά

Hrvatska

Česká republika

Danmark

Polska

România

Sverige

Personal tools