Question 13 Bob and Barb operate a small bed and breakfast w

Question 13

Bob and Barb operate a small bed and breakfast with three rooms. They charge $190 per night for each room. Over the years, they have developed the following probability distribution for the number of rooms rented per night in April, which we will call X. The distribution is shown below.

Find their expected nightly April revenue to two decimal places. Hint 1: Revenue = price * quantity. Hint 2: If c is any constant, E(cX) = cE(X).

Solution

Consider the table:      
      
x   P(x)   x P(x)
0   0.1   0
1   0.2   0.2
2   0.6   1.2
3   0.1   0.3
      
Thus,      
      
E(x) = Sum(x P(x)) = 1.7, which is the mean number of rooms.

Thus, the mean revenue is 1.7*$190 = $323.00 [ANSWER]