1. Chapter 5: Discrete Probability Distributions

2. I. Random Variables
RV’s are numerical descriptions of the outcome of an experiment. They can be discrete or continuous.

3. A. Discrete RV’s
Either a finite # of values or an infinite sequence of values.

4. B. Continuous RV May assume any numerical value in an interval or
collection of intervals.
Examples: measurements of time, weight, distance
and temperature.
An experiment that generates a continuous RV might be the amount of time a person spends in the line at Rally’s.

5. II. Discrete Probability Distributions
Describes how probabilities are distributed over the values of the random variable.
A. Probability function
For a discrete r.v. x, the probability distribution is defined by f(x), the d.p.f.
f(x)0

6. B. Example
The Wall Street Journal takes a survey to get an idea of the size of the households that subscribe.

7. f(x) is the probability that x will take the value 1,2,3,4, or 5.

8. III. Expected Value and Variance
To this point we have calculated measures of location and dispersion for samples of data. We can do the same with the values of a random variable.

9. A. Expected Value
This is the measure of central location (mean) for the random variable.
In the WSJ example:
E(x) = 1(.127)+2(.446)+3(.168)+4(.140)+5(.119)
E(x)=2.678 members in the randomly chosen household.

10. B. Variance
Summarizes the variability in the values of the random variable.
In the WSJ example, Var(x)=
The standard deviation is the square root, or =1.91.
This means that on average, a household deviates from 2.68 members by almost 2 members.