One recognizes the integrand of Equation (23) as a r(a, 6) density, hence M (t) = (;)"(1) = (24) |3| (1 - Bt)a Exercise 5. Verify the algebra leading from Equation (22) to Equation (23).
One recognizes the integrand of Equation (23) as a r(a, 6) density, hence M (t) = (;)"(1) = (24) |3| (1 - Bt)a Exercise 5. Verify the algebra leading from Equation (22) to Equation (23).
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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Transcribed Image Text:Example: The Gamma Distribution
Suppose X ~ T(a, B), then
M(t) =
dx
BaT(a)
22
Now we do a little high school algebra. Define & =
Then one may write
1-Bt"
Equation (22) as:
M(t) = ()ª /
(23)
dx
One recognizes the integrand of Equation (23) as a r(a, 6) density, hence
8.
M(t) = (Gr"(1) = (1 - AY•
(24)
(1 – Bt)a
Exercise 5. Verify the algebra leading from Equation (22) to Equation (23).
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