Suppose a store sells two different coffee makers of a particular brand, a basicmodel selling for $30 and a fancy one selling for $50. Let X be the number of people amongthe next 10 purchasing this...

Suppose a store sells two different coffee makers of a particular brand, a basic
model selling for $30 and a fancy one selling for $50. Let X be the number of people among
the next 10 purchasing this brand who choose the fancy one. Suppose that the choices are
independent and have the same probability.
(a) (5 points) Precisely state the distribution of X.
(b) (5 points) Calculate the probability that at most 2 purchases are the fancy ones in the
next 10 purchasing.
(c) (5 points) Let Y be the revenue of the next 10 purchasing. Write Y as a function of X.
(d) (5 points) Calculate the probability that the revenue is at least $470.
(e) (5 points) Find the mean and variance of the revenue Y .