4. (a) Let W X₁ + X₂ +...+ X₁, be a sum of h mutually independent and identically distributed exponential random variables with mean . Show that W has a gamma distribution with mean he. (b) Let X₁, X₂, X3 denote a random samples of size 3 from gamma distribution with a 7 and 0=5. (i) Find the moment generating function of Y = X₁ + X₂ + X3. (ii) How is Y distributed?

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...
icon
Related questions
Question

4.

4. (a) Let W X₁ + X₂ +...+ X₁, be a sum of h mutually independent and identically
distributed
exponential random variables with mean . Show that W has a gamma
distribution with mean he.
(b) Let X₁, X₂, X, denote a random samples of size 3 from gamma distribution with
a
7 and 05.
(i) Find the moment generating function of Y = X₁ + X₂ + X3.
(ii) How is Y distributed?
Transcribed Image Text:4. (a) Let W X₁ + X₂ +...+ X₁, be a sum of h mutually independent and identically distributed exponential random variables with mean . Show that W has a gamma distribution with mean he. (b) Let X₁, X₂, X, denote a random samples of size 3 from gamma distribution with a 7 and 05. (i) Find the moment generating function of Y = X₁ + X₂ + X3. (ii) How is Y distributed?
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON