2. Your company maintains a fleet of two planes that it leases out to its customers on a monthly basis. The demand distribution for planes is as follows:

Demand (planes per month) 0, 1, 2, 3, 4

Probability x=0: 0.10, x=1: 0.25, x=2: 0.30, x=3: 0.25, x=4: 0.10

a. What is the expected demand per month? (0.5 points)

b. What is the variance of the demand per month? (0.5 points)

The fixed cost of maintaining a plane in your fleet is $100,000 per plane per month regardless of whether the plane is leased out or not. The lease revenue is $200,000 per plane per month. All additional expenses of operating a leased plane are borne by the customer. (Use this information in parts c and d of this question.)

c. What is your company's expected profit per month? (1 point)

d. What is the standard deviation of profit per month? (0.5 points)