a. Find the moment-generating function of Y = X₁ + X₂ + ... + X₁. b. What is the distribution of the random variable Y?
a. Find the moment-generating function of Y = X₁ + X₂ + ... + X₁. b. What is the distribution of the random variable Y?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![Let X₁, X₂, ..., X, be independent exponential
random variables with parameter 1.
a. Find the moment-generating function of
Y = X₁ + X₂ + + X₁.
b. What is the distribution of the random
variable Y?
My(t)
=
(₁²₁)
; beta
t
distribution
My(t)
=
(²)
; Poisson
r
distribution
r
My(t)
=
(₁=1)
distribution
My(t):
(₁4₁)
+ t
distribution
My(t)
=
(²)
distribution
O
=
; normal
; binomial
; gamma](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcbef974-bbb6-4c1a-bded-5f7edf6bae7b%2F7892c96d-e46f-4ef5-af2a-327ff7688676%2Fgf4ybos_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X₁, X₂, ..., X, be independent exponential
random variables with parameter 1.
a. Find the moment-generating function of
Y = X₁ + X₂ + + X₁.
b. What is the distribution of the random
variable Y?
My(t)
=
(₁²₁)
; beta
t
distribution
My(t)
=
(²)
; Poisson
r
distribution
r
My(t)
=
(₁=1)
distribution
My(t):
(₁4₁)
+ t
distribution
My(t)
=
(²)
distribution
O
=
; normal
; binomial
; gamma
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