B A sum of RM50,000 is invested at a rate R, selected from a uniform distribution on the interval (0.03, 0.07). Once R is selected, the sum is compounded instantaneously for a year, so that 50000 R X e = (in ringgit) is the amount at the end of that year. Find the cumulative distribution function and probability density function of X.

(c) Let 1 2 3 4 5 X X X X X , , , , be a random sample of size 5 from a geometric distribution with 1 3 p = . Find the moment generating function of Y X X X X X = + + + + 1 2 3 4 5 . Hence, determine the probability distribution for Y