Random Variable

A rule that assigns a number to each outcome in the sample space is called a random variable. Random Variables denoted by letters at the end of the alphabet: X,Y,Z.

Examples Select an individual at random, measure weight each outcome generates a # Select 5 individuals at random, count the # who watched TV last night The observed value is random and variable from sample to sample or item to item.

Types of random variables Discrete: potential values separated points on the number line generally counting Continuous: potential values fall in an interval on number line generally measured

Probability Distributions; Discrete Variables   For Discrete Random Variables we assign probabilities to the discrete points

The collection of P(x) values for all possible x values is the probability distribution.

Summarizing probability distribution The mean (expected value) of a discrete random variable is This is the average value of X if the experiment is performed an extremely large number of times.

The variance of a discrete random variable is   The standard deviation is