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1. Show that the rth moment about the origin of the gamma distribution is 3"T(a+r) T(a) Hint: Substitute y = x/B in the integrating defining u', and then use the gamma function to evaluate the integral.

1. Show that the rth moment about the origin of the gamma distribution is 3"T(a+r) T(a) Hint: Substitute y = x/B in the integrating defining u', and then use the gamma function to evaluate the integral.

A First Course in Probability (10th Edition)
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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1. Show that the rth moment about the origin of the gamma distribution is Hi = 3"T(a+r) T(a) Hint: Substitute y = x/B in the integrating defining u', and then use the gamma function to evaluate the integral. 2. A random variable X has the discrete uniform distribution SE 1= 1,2,...,k, f(x; k) = {6. elsewhere. Show that the moment-generating function of X is e*(1 – ekt) k(1 – et) Mx(t) : 3. A random variable X has the Poisson distribution p(x; µ) = e-"u® /æ! for x = 0,1, 2, . Show that the moment-generating function of X is Mx (t) = e"(e? –1)
Transcribed Image Text:1. Show that the rth moment about the origin of the gamma distribution is Hi = 3"T(a+r) T(a) Hint: Substitute y = x/B in the integrating defining u', and then use the gamma function to evaluate the integral. 2. A random variable X has the discrete uniform distribution SE 1= 1,2,...,k, f(x; k) = {6. elsewhere. Show that the moment-generating function of X is e*(1 – ekt) k(1 – et) Mx(t) : 3. A random variable X has the Poisson distribution p(x; µ) = e-"u® /æ! for x = 0,1, 2, . Show that the moment-generating function of X is Mx (t) = e"(e? –1)
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