dt" It=0 Exercise 4. Show that if X is a normal random variable, then the parameters u and o? in Equation (26) are indeed the expected value and variance of X, respectively, by applying Theorem 11 to the MGF of the normal distribution, which is given by Equation (27). 10

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Theorem 11. For any interger r > 0,
d" Mx
= E[X"]
(21)
dtr
It%3D0
Exercise 4. Show that if X is a normal random variable, then the parameters
u and o? in Equation (26) are indeed the expected value and variance of X,
respectively, by applying Theorem 11 to the MGF of the normal distribution,
which is given by Equation (27).
10
Transcribed Image Text:Theorem 11. For any interger r > 0, d" Mx = E[X"] (21) dtr It%3D0 Exercise 4. Show that if X is a normal random variable, then the parameters u and o? in Equation (26) are indeed the expected value and variance of X, respectively, by applying Theorem 11 to the MGF of the normal distribution, which is given by Equation (27). 10
Exercise 3. If X and Y are independent Poisson random variables with
parameters ui and u2. Prove that W = X +Y_is Poisson with parameter
Transcribed Image Text:Exercise 3. If X and Y are independent Poisson random variables with parameters ui and u2. Prove that W = X +Y_is Poisson with parameter
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