Answered: 4. Show that if a random variable has a…

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.

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

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 23E

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Question

#1 - homework question practice problem from textbook

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
(b)
α
7+1 (³₂²)
2
when r is even.

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Step 2: Define uniform distribution and calculate r th moment:

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Step 3: Calculate rth moment about mean when r is odd:

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Step 4: Calculate rth moment about mean when r is even:

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