2. Let X the exponential random variable with parameter 1. (a) Show, by deriving from the definition, that the moment-generating function of X is Mx (1) =- 入-t (b) Using an appropriate property, derive from the formula mentioned in (a) to find the 1 general formula of E(X") for k= 1,2,..Then verify that E(X)=and V(X)=-
2. Let X the exponential random variable with parameter 1. (a) Show, by deriving from the definition, that the moment-generating function of X is Mx (1) =- 入-t (b) Using an appropriate property, derive from the formula mentioned in (a) to find the 1 general formula of E(X") for k= 1,2,..Then verify that E(X)=and V(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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![12. Let X the exponential random variable with parameter å.
(a) Show, by deriving from the definition, that the moment-generating function of X is
Mx (t) =-
入-t
(b) Using an appropriate property, derive from the formula mentioned in (a) to find the
1
general formula of E(X*) for k=1,2,.Then verify that E(X)=-and V(X)=
え](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c985735-1712-4ec8-b727-d5bdfdaddb93%2F6941f0a0-bc62-4fab-ab26-e58932ca6958%2F5nqrk2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:12. Let X the exponential random variable with parameter å.
(a) Show, by deriving from the definition, that the moment-generating function of X is
Mx (t) =-
入-t
(b) Using an appropriate property, derive from the formula mentioned in (a) to find the
1
general formula of E(X*) for k=1,2,.Then verify that E(X)=-and V(X)=
え
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