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?
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...
Related questions
Question
4.
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
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON