1. Random Variable

2. 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.

3. 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.

4. 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

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

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

7. 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.

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