Picard Partners is planning a major investment. The amount of profit X is uncertain but the research department has

provided the following probability distribution for X (in millions of dollars):

X 1 2 4 10

P(X) 0.2 0.5 0.2 0.1

(a) Find and interpret the mean of X.

(b) Find and interpret the standard deviation of X.

(c) Picard owes its source of capital a fee of $200,000 plus 10% of the profits X. So the firm actually retains Y = 0.9X -

0.2 from the investment. Use a linear transformation of your results in A. and B. to find the mean and standard deviation

for Y.

(d) Assume the data for this problem are Normal, what is the probability that Picard retains more than $2.75 million?