Let the random variable X be the number of days that a randomly selected patient needs to be in the hospital. Suppose X has the p. m. f. f(x) = (5-x)/9 for x=1,2,3 (= 0 otherwise) (a) (1 point) Find the cdf, F(x), of X. (b) (2 points) If the patient is to receive $500 from an insurance company for the first day in the hospital and $300 for each day thereafter, what is the expected payment for the hospitalization?4. Twenty percent of the customers at a Giant supermarket purchase something at the Deli department. (a) (1 point) What is the probability that exactly three of the next eight Giant supermarket shoppers buy something at the Deli? (b) (1 point) What assumption(s) are you making in the calculation in part (a)?