The amount of bread (in hundreds of pounds) that a certain bakery is able to sell in a day is found to be a numerical-valued random phenomenon, with a probability function specified by the probability density function (.), given by
(i) Find the value of A which makes f(.) a probability density function.
(ii) Graph the probability density function.
(iii) What is the probability that the number of pounds of bread that will be sold tomorrow is (a) more than 500 pounds, (b) less than 500 pounds, (c) between 250 and 750 pounds?
(iv) Denote, respectively, by A, B, and C, the events that the number of pounds of bread sold in a day is (a) greater than 500 pounds, (b) less than 500 pounds, (c) between 250 and 750 pounds. Find P[A I B], P[A | C]. Are A and B independent events? Are A and C independent events?