=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. =

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
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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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