Question: The steps in this exercise lead to the probability density function of an Erlang random variable X with parameters and r, f(x) = r xr1

The steps in this exercise lead to the probability density function of an Erlang random variable X with parameters λ and r, f(x) = λr xr–1 e–λ /(r – 1) !, x > 0, r = 1, 2, . ..
(a) Use the Poisson to express P(X > x).
(b) Use the result from part (a) to determine the cumulative function of X.
(c) Differentiate the cumulative functions in part (b) and simplifies to obtain the probability density function of X.

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