Math 225 Course Notes

Section 4.2: Probability Distributions of Discrete Random Variables

Key Concepts

The distribution of discrete random variables can be displayed in a table or with a formula. The sum of the probabilities of the possible values is one, and all probabilities are between 0 and 1. Cumulative probability distributions are an alternative way to display the distributions of random variables.

Discrete Distributions

Example: 
    x  |  3  |  4  |  5  |  6
-------------------------------
P(X=x) | .2  | .3  | .4  | .1
Capital letters represent random variables. Small letters represent the possible values of random variables.

In this example, the random variable X has four possible values; 3, 4, 5, and 6.

The probability that the X is 4 equals .3, or P(X = 4) = 0.3.

The sum of all the probabilities of all the possible values is one, and all probabilities are between zero and one.

Example: Sometimes, instead of writing out the whole table, the distribution is specified by a formula. 

P( X = x ) = x/10    for x = 1,2,3, or 4
In a table, this would be 
    x  |  1    |  2    |  3    |  4
--------------------------------------
P(X=x) | 1/10  | 2/10  | 3/10  | 4/10

Cumulative Distributions

The cumulative probability distribution function tells P(X <= x).

In the two previous examples, here are the cumulative probability distributions.

Example 1: 

   x   | P(X <= x)
----------------
   3   |   .2
   4   |   .5
   5   |   .9
   6   |  1.0
Example 2: 
   x   | P(X <= x)
----------------
   1   |   .1
   2   |   .3
   3   |   .6
   4   |  1.0
Last modified: Feb 5, 1996

Bret Larget, larget@mathcs.duq.edu