Discrete Distribution Dice Game Problem 
A dice game pays a player $5
for rolling a 3 or 5with a single die. The player must pay $2 for rolling
anything else. What is the mean and standard deviation of the distribution.
Draw the distribution. * Solution: 
probability of rolling a 3 or 5 = 1/6 +
1/6 

= 1/3 

prob. of rolling 1, 2, 4, 6 = 1/6 + 1/6 +
1/6 + 1/6 
= 2/3 

mean = Σ x_{i }p_{i} 
= (  2 ) 2/3 + ( 5 ) 1/3 


variance = [( 2 1/3 )^2 ]
∙ 2/3 + [( 5 1/3 )^2 ] ∙
1/3 
= 10.89 

standard deviation = ( 10.89)^0.5 

standard deviation = 3.30 




* The numbers in this
problem were taken from Prepare for the AP Exam Guide for Yates, Moore, and
Starnes's Practice of Statistics, #30, Exam 4, 2003 