A highway engineer knows that his crew can lay 5 miles of hi

A highway engineer knows that his crew can lay 5 miles of highway on a clear day, 2 miles on a rainy day, and only 1 mile on a snowy day. Suppose the probabilities are as follows: A clear day: .6, a rainy day: .3, a snowy day: .1. What are the mean and variance?

Solution

Consider the table:          
          
x   P(x)   x P(x)   x^2 P(x)
5   0.6   3   15
2   0.3   0.6   1.2
1   0.1   0.1   0.1
          
Totals       3.7   16.3
       =E(x)   =E(x^2)
          
Thus,          
          
E(x) =    3.7 [MEAN]

Var(x) = E(x^2) - E(x)^2 =    2.61   [VARIANCE]