http://www.ck12.org Chapter 3. Introduction to Discrete Random Variables
We can see the values ofP(X)if we press
TRACE. Look at the screenshot below. You can see the value ofP(X) = 0 .25 forX=0.
It’s clear that the histogram shows the probability distribution for the discrete random variable. In other words,
P( 0 )gives the probability that the discrete random variable is equal to 0,P( 1 )gives the probability that the discrete
random variable is equal to 1, andP( 2 )gives the probability that the discrete random variable is equal to 2. Notice
that the probabilities add up to 1. One of the rules for probability is that the sum of the probabilities of all the
possible values of a discrete random variable must be equal to 1.
Example C
Does the following table represent the probability distribution for a discrete random variable?
X 0 1 2 3
P(X) 0. 1 0. 2 0. 3 0. 4
Yes, it does, since∑P(X) = 0. 1 + 0. 2 + 0. 3 + 0 .4, or∑P(X) = 1 .0.
Guided Practice
Say you are going to spin a spinner 3 times and that the colors red and blue are equally represented. Show the
probability distribution for these spins.
Answer:
Let the variableXbe the number of times your spinner lands on red. The table below lists all of the possible events
that can occur from the spins.
TABLE3.7:
Trial First Spin Second Spin Third Spin X
1 R R R 3
2 R R B 2
3 R B R 2
4 R B B 1
5 B R R 2
6 B B R 1
7 B R B 1
8 B B B 0