The steps in this exercise lead to the probabil- ity density function of an Erlang random variable X' with parameters and r, f(x) = x'x '^(-1),x>0. and = 1,2.....

(a) Use the Poisson distribution to express P{X> x).

(b) Use the result from part

(a) to determine the cumu- lative distribution function of .X.

(e) Differentiate the cumulative distribution function in part

(b) and simplify to obtain the probability den- sity function of X.