=tX > 0. The random variable X has moment generating function 1 Mx(t): t<λ. " [1 − (t/X)]² ¹ Use this moment generating function to find the mean and variance of X. =

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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b) Explain how X can be related to the exponential distribution by using a moment generating function argument.

Let λ > 0. The random variable X has moment generating function
1
Mx (t)
=
t<λ.
[1 − (t/X)]² ¹
(a) Use this moment generating function to find the mean and variance of X.
Transcribed Image Text:Let λ > 0. The random variable X has moment generating function 1 Mx (t) = t<λ. [1 − (t/X)]² ¹ (a) Use this moment generating function to find the mean and variance of X.
(b) The exponential distribution with rate parameter λ > 0 has moment generating
function
\
M (t)
=
t<\.
\ − t'
Transcribed Image Text:(b) The exponential distribution with rate parameter λ > 0 has moment generating function \ M (t) = t<\. \ − t'
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