Annual profit (P) is the product of total annual sales (S) and profit per unit sold (X); thatis, P=XS. 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 areindependent). What are themean, variance, and standard deviation of the probability distribution for annualprofit, P?

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). What are the mean, variance, and standard deviation of the probability distribution for annual profit, P? X (Unit Profit) S (Annual Sales) Value Probability Value Probability 0.15 6 0.4 0.35 0.2 W N - 0 0.40 0.4 0.10 The mean is (Round to two decimal places.) The variance is . (Round to three decimal places.) The standard deviation is . (Round to two decimal places.)