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4. Show that if a random variable has a uniform density with the parameters a and ß, the rth moment about the mean equals (a) 0 when r is odd; r 1 α (b) β-α 2 r+1 when r is even.

4. Show that if a random variable has a uniform density with the parameters a and ß, the rth moment about the mean equals (a) 0 when r is odd; r 1 α (b) β-α 2 r+1 when r is even.

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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**Problem 4:** Show that if a random variable has a uniform density with the parameters \( \alpha \) and \( \beta \), the \( r \)th moment about the mean equals: (a) 0 when \( r \) is odd; (b) \(\dfrac{1}{r+1} \left( \dfrac{\beta - \alpha}{2} \right)^r\) when \( r \) is even.
Transcribed Image Text:**Problem 4:** Show that if a random variable has a uniform density with the parameters \( \alpha \) and \( \beta \), the \( r \)th moment about the mean equals: (a) 0 when \( r \) is odd; (b) \(\dfrac{1}{r+1} \left( \dfrac{\beta - \alpha}{2} \right)^r\) when \( r \) is even.
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