CK-12 Probability and Statistics - Advanced

4.2. Probability Distribution for a Discrete Random Variable http://www.ck12.org

Lesson Summary

1. Theprobability distributionof a discrete random variable is a graph, a table, or a formula that specifies the
   probability associated with each possible value that the random variable can assume.


2. All probability distributions must satisfy:

P(x)>0 (for all values ofx)

∑

x

P(x) = 1

Review Questions

1. Consider the following probability distribution:

x − 4 0 1 3

p(x) 0. 1 0. 3 0. 4 0. 2

a. What are all the possible values ofx?

b. What value ofxis most likely to happen?

c. What is the probability thatxis greater than zero?

d. What is the probability thatx=−2?

2. A fair die is tossed twice and the up face is recorded. Letxbe the sum of the up faces.
   a. Give the probability distribution ofxin tabular form.
   b. What isp(x≥ 8 )?
   c. What isp(x< 8 )?
   d. What is the probability thatxis odd? Even?
   e. What isp(x= 7 )?


3. If a couple has three children, what is the probability that they have at least one boy?

Review Answers

1. 1.x={− 4 , 0 , 1 , 3 };
   2. 1;
   3. 0.6;
   4. 0
   
   
   1. 
      
   
   
   
   

x 2 3 4 5 6 7 8 9 10 11 12

p(x) 1 / 36 2 / 36 3 / 36 4 / 36 5 / 36 6 / 36 5 / 36 4 / 36 3 / 36 2 / 36 1 / 36

2. 15/36;


3. 21/36;


4. 18/ 36 , 18 /36;