Amedical insurance plan reimburses $100 per day, up to a maximum of five days, for each day the policy

holder is hospitalized. it is estimated that the probability that any person is hospitalized for exactly one

day is 0.001, for exactly two days is 0.002, for exactly three days is 0.003; for exactly four days is 0.004,

and for five or more days 0.008. the annual premium is $10.

(a) construct the probability distribution for x, the number of days hospitalized.

(b) find the mean number of days hospitalized.

(c) construct the probability distribution for y, the profit (or loss) of each policy.

(d) if fifty thousand of such policies were sold, find the expected profit (or loss).