6. Using the moment generating function for a Poisson random variable having pdf e-2x fx(x) = x = 0, 1,... Use My(t) to verify that E(X) = 1 and Var (X) = 1. 7. Let X and Y be two independent exponential random variables with pdf's fx(x) = (-) e-x/₂ x>0 And fx(x) = (-)e-v/A y>0 Let Z = X + Y. Does Z have an exponential distribution?
6. Using the moment generating function for a Poisson random variable having pdf e-2x fx(x) = x = 0, 1,... Use My(t) to verify that E(X) = 1 and Var (X) = 1. 7. Let X and Y be two independent exponential random variables with pdf's fx(x) = (-) e-x/₂ x>0 And fx(x) = (-)e-v/A y>0 Let Z = X + Y. Does Z have an exponential distribution?
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
Section13.3: Special Probability Density Functions
Problem 30E
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Transcribed Image Text:6. Using the moment generating function for a Poisson random variable having pdf
e-2x
fx(x) =
x = 0, 1,...
Use My(t) to verify that E(X) = 1 and Var (X) = 1.
7. Let X and Y be two independent exponential random variables with pdf's
fx(x) = (-) e-x/₂
x>0
And
fx(x) = (-)e-v/A
y>0
Let Z = X + Y. Does Z have an exponential distribution?
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