Answered: Exercise 2. Let X1, X2, , Xn be… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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Exercise 2. Let X1, X2, , Xn be independent erponential random vari-
ables with the same parameter ). Using induction, show that the density of
X = X1+ X2+··.
...
+ Xn is
fn (x) =
(n- 1)1"-le-
(17)
%3D
( Recall this is the Erlang distribution, a special case of the Gamma distri-
bution.)

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