# S2 Revision Notes Edexcel

A summary of everything you need to know for the S2 exam

- Created by: Karina Gahir
- Created on: 28-03-13 10:20

First 443 words of the document:

Karina Gahir

S2 EDEXCEL REVISION NOTES

Binomial Distribution

Binomial probability distribution is defined as:

o P(X=r) = nCr x pn x (1-p)n-r

o Distribution is written as: X~B(n,p)

Conditions include:

o Fixed number of trials

o All trials are independent of one another

o Probability of success remains constant

o Each trial much have the same two possible outcomes

E(X) = np

Var(X) = npq [where q = 1 - p]

SD(X) = V ar (X ) = npq

To calculate the probabilities:

o P(X x) = read off the tables

o P(X x) = 1- P(X x-1)

o P(X < x) = P(X x-1)

o P(X > x) = 1- P(X x)

o P(x X y) = P(X y) P(X x-1)

o P(x < X < y) = P(X y) P(X x)

o P(x X < y) = P(X y-1) P(X x-1)

o P(x < X y) = P(X y) P(X x)

Note: If p > 0.5, need to make X~B(n,p) convert to Y~B(n,p)

Example:

If X~B(18,0.9), 0.9 is > 0.5 therefore not on the tables

We want to find P(X > 8)

This will become P(Y < 10) AND Y~B(10,0.1)

Poisson Distribution

Binomial probability distribution is defined as:

e- x r

o P(X=r) = r!

o Distribution is written as: X~Po( )

Conditions include:

o Events occur at random

o All events are independent of one another

o Average rate of occurrence remains constant

o Zero probability of simultaneous occurrences

E(X) =

Var(X) =

SD(X) = V ar (X ) =

To calculate the probabilities:

o P(X x) = read off the tables

o P(X x) = 1- P(X x-1)

o P(X < x) = P(X x-1)

o P(X > x) = 1- P(X x)

o P(x X y) = P(X y) P(X x-1)

o P(x < X < y) = P(X y) P(X x)

o P(x X < y) = P(X y-1) P(X x-1)

o P(x < X y) = P(X y) P(X x)

To approximate the poisson to the binomial, the following conditions have to apply:

o If X~B(n,p) and 1) n is large [n > 50] and

2) p is small [p < 0.1] then, X~Po(np)

## Comments