Please show the full steps. The gamma distribution is a family of continuous probability distributions withpositive parameters r, A and a density given byx"-le-Ax_I(r)f(x) =when x > 0, and zero otherwise.||Here I(r) is called the gamma function and defined by T(r) = S x"-le¬®dx. Seehttps://en.wikipedia.org/wiki/Gamma.function for more details.Say X -on the properties of gamma distributions.gamma(r, X) if X has the density above. The following problems are The gamma function is a fundamental function in mathematics. Oneof its many amazing properties is thatГ(п) — (п — 1)!, for n %3= 1,2, ....Thus the gamma function is a generalization of the factorials. Let us prove thisidentity using probability following these steps.(i) Take r = n, 1 = 1 and find E(X) either using problem 2 or problem 3.(ii) Show that E(X) is also the ratio I(n+ 1)/T(n).(iii) Use induction now to complete the argument.

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Description: Please show the full steps. The gamma distribution is a family of continuous probability distributions withpositive parameters r, A and a density given byx"-le-Ax_I(r)f(x) =when x > 0, and zero otherwise.||Here I(r) is called the gamma function and d

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Math

Probability

Please show the full steps.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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