The following distribution was collected over a 1000 days fo

The following distribution was collected over a 1000 days for the number of complaints for a local restaurant. What is the expected number of complaints for this restaurant.

Number of complaints 0 1 2 3 4 5

P(X) .08 .1 .15 .2 .25 .22

Solution

Expected complaints,

E(x) = Sum( x* P(x) )

E(x) = 0*0.08 + 1*0.1 + 2*0.15 + 3*0.2 + 4*0.25 + 5*0.22

E(x) = 3.1