3.X = the number of cars that a dealer sells in a day is a random variable with probability distribution shown in the accompanying table:

x	0	1	2	3	4	5
p(x)	0.10	0.15	0.20	0.30	0.20	0.05

a. According to the above distribution, there is a 20% chance that the dealer will sell 2 cars in a day. (p(2) = 0.20). This probability is based on past data. Explain why this is an estimate, not the exact probability. [2 marks]

b. Calculate E(X) and explain what the number means. [3 marks]

c. Refer to the above problem. Suppose the dealer makes a profit of $700 for each car it sells, and it cost them $1000 per day to operate the lot regardless of the number of cars sold. Determine the probability distribution of Y = net profit per day. [3 marks]

d. What is the probability that the dealer will lose money on any given day? [1 mark]