CK-12 Probability and Statistics - Advanced

4.3. Mean and Standard Deviation of Discrete Random Variables http://www.ck12.org

Review Questions

1. Consider the following probability distribution:

x 0 1 2 3 4

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

Figure:The probability distribution for question 1.

a. Find the mean of the distribution.

b. Find the variance.

c. Find the standard deviation.

2. An officer at a prison questioned each inmate to find out how many times the inmate has been convicted. The
   officer came up with the following table that shows the relative frequencies ofx:

x 0 1 2 3 4

p(x) 0. 16 0. 53 0. 20 0. 08 0. 03

Figure:The probability distribution for question 2. If we regard the relative frequency as approximately the

probability, what is the expected value of the number of times of previous convictions of an inmate?

Review Answers

1. 
   
   
   
   1. 1.7;
   
   
   2. 1.21;
   
   
   3. 
      
      
      
      1. 1
      
      
      
      
   
   
   
   


2. 
   
   
   
   1. 29