# S1 Statistics Revision - Chapter 8 Notes

Chapter 8 - Discrete random variables

- Created by: Megan Wilkinson
- Created on: 17-05-12 21:19

First 206 words of the document:

AS Statistics Revision

Statistics 1 Chapter 8

Discrete Random Variables

Key points to remember

Random variable X = a variable that represents the values

obtained when we take a measurement from an experiment in

the real world.

Discrete random variable = a variable that changes by steps,

and

takes only specified values in any given interval.

Probability function = a function that describes how the

probabilities are assigned

Probability distribution = the set of all the values of a random

variable together with their associated probabilities. For

example:

X 1 2 3 4 5 6

P(X=x) 1/6 1/6 1/6 1/6 1/6 1/6

is the probability distribution which describes the values, x,

taken

when a die is thrown and the associated probabilities. Note

P(X=x) is sometimes written as p(x).

Sum of all probabilities = p(x) = 1

The expected value of X = E(X) = xP(X=x) = xp(x)

The expected value for X² = E(X²) = x²P(X=x)

The Variance of X = Var(X) = E(X²) ((E(X))²

Expectation of a linear function of X = E(aX + b) aE(X) + b

Variance of a linear function = Var(aX + b) a² Var(X)

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