Salesperson visits from house to house to sell her knives. The probability that she makes a sale at a random house is .3. Given that she makes a sale, the sale is worth $100 with probability .6 and $200 with probability .4. Suppose that the salesperson visits five houses on a given day.

problem1) Find the probability that she makes exactly two sales?

problem2) Find the probability that she sells exactly $100 worth of knives?

Querstion3) Given that exactly two visits (out of the five) are sales, find

(a) the probability distribution of her sales value
(b) the expected sales value
(c) the variance and standard deviation of her sales value

problem4) Given that she has sales volume of exactly $200, find

(a) probability distribution of the number of sales that she makes

(b) expected number of sales that she makes?

Let X, Y, and Z refer to the three random variables. It is given that Var(X) = 4, Var(Y) = 9, and Var(Z) = 16. It is further known that E(X) = 1, E(Y) = 2, and E(Z) = 4. Furthermore E(XY) = 7, E(XZ) = 12, and E(YZ) = 15.

problem5) Find Var(X-Y)

problem6) Find Corr(X,Z)

problem7) Find Cov(2X+Y,4Z)

problem8) Find E(3X+4Y-5Z)