d) Use the moment generating function to find E[X], verifying your answer to part b). e) Find E[X2] directly. f) Use the moment generating function to find E[X2].
d) Use the moment generating function to find E[X], verifying your answer to part b). e) Find E[X2] directly. f) Use the moment generating function to find E[X2].
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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Question
Do parts d-g
![1. Consider the function f(x) = (x+1)²/15 for x = -2, -1, 0, 1, 2
a) Verify that the function is a pdf.
b) Find E[X] directly, that is evaluate sum[x*f(x)]
c) Find the moment generating function for X.
d) Use the moment generating function to find E[X], verifying your answer to part b).
e) Find E[X2] directly.
f) Use the moment generating function to find E[X²] .
g) Find the variance of X and the standard deviation of X.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09fcf446-1afb-4b15-acb5-39347ac88924%2Fdb436589-9c50-48d6-a8ed-28d280adf695%2Fvlxgx89_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the function f(x) = (x+1)²/15 for x = -2, -1, 0, 1, 2
a) Verify that the function is a pdf.
b) Find E[X] directly, that is evaluate sum[x*f(x)]
c) Find the moment generating function for X.
d) Use the moment generating function to find E[X], verifying your answer to part b).
e) Find E[X2] directly.
f) Use the moment generating function to find E[X²] .
g) Find the variance of X and the standard deviation of X.
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Step 1
We want to find E(X) and E(X2) by moment generating function
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