i) Find the cumulative distribution function (CDF) of X. 8 ii) Show that the moment generating function (MGF) of X is M(t) = 8-t iii) Use the MGF in (ii) to find the mean and variance of X. .

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 14E
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b)
A random variable X follows an exponential distribution, X~Exp(0), with parameter 0 > 0.
Find the cumulative distribution function (CDF) of X.
i)
ii)
Show that the moment generating function (MGF) of X is M(t)
=
iii)
Use the MGF in (ii) to find the mean and variance of X.
Transcribed Image Text:b) A random variable X follows an exponential distribution, X~Exp(0), with parameter 0 > 0. Find the cumulative distribution function (CDF) of X. i) ii) Show that the moment generating function (MGF) of X is M(t) = iii) Use the MGF in (ii) to find the mean and variance of X.
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