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 e (r 1) , x 0, r 1, 2, (a) Use the Poisson distribution to express P(X x) (b) Use the result from part (a) to determine the cumulative distribution function of X (c) ...

a PX x implies that there are r 1 or less counts in an int ...

The steps in this exercise lead to the probability density function of an Erlang random variable X

Question:

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.
Distribution
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