Problem
Annual profit (P) is the product of total annual sales (S) and profit per unit sold (X); that is, P = X · S. It is desired to know the probability distribution of the random variable P when X and S have the following assumed probability mass functions (X and S are independent):
X (Unit Profit) S (Annual Sales)
Value Probability Value Probability
0 0.05 5 0.4
1 0.45 6 0.2
2 0.30 8 0.4
3 0.20
What are the mean, variance, and standard deviation of the probability distribution for annual profit, P?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.