Gabelli Partners is planning a major investment. The amount of profit X is uncertain but a probabilistic estimate gives the following distribution (in millions of dollars):

Profit 1, 1.5, 2, 4, 10

Probability 0.1, 0.2, 0.4, ??, 0.1

a. Find P(X = 4) = 0.2

b. Find the mean profit and the standard deviation of the profit.

c. Gabelli Partners owes its source of capital a fee of $200,000 plus 10% of the profits X. So thefirm actually retains Y = 0.9X 0.2 from the investment. Find the mean and standard deviation of Y

Please explain the steps! Thank you!