A convenience store prepared 60 sandwiches that were very popular with its customers for the week's sales. The demand for these sandwiches is a random variable denoted by X.

Suppose that the probability distribution of X looks like this (X = Request for sandwiches (in unit)) :

X = 0 ; Probability = 0,10

X = 40 ; Probability = 0,20

X = 60 ; Probability = 0,40

X = 80 ; Probability = 0,20

X = 100 ; Probability = 0,10

A) What is the expectation of X?

B) What is the variance of X?

C) What is the standard deviation of X?

D) What is the probability that the demand is strictly greater than the quantity of sandwiches prepared?

E) Each sandwich is priced at $ 3 while its cost is valued at $ 2.25. What are the amount of profit corresponding to each possible value of the request (put a negative value in the case of a loss)?

F) What is the convenience store's expected profit from selling the sandwiches this week?

G) What is the probability that the convenience store will experience a loss this week (i.e. find P (Y <0))?