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Chapter 4: Q4.4-2E (page 240)

IfXhas the uniform distribution on the interval [a, b], write a formula for every even central moment ofX.

Short Answer

Expert verified

The fifth central moment of X is 0.

Step by step solution

01

Given information

X follows a uniform distribution.

02

State p.d.f and compute the central moment

The p.d.f of X is

\(f\left( x \right) = \frac{1}{{b - a}};a < x < b\)

\(E\left( x \right) = \mu = \left( {\frac{{a + b}}{2}} \right)\)

Since uniform p.d.f is symmetric with respect to its mean.

So,

\(\begin{array}{l}E\left[ {\left( {X - \mu } \right)} \right] = 0\\ \Rightarrow E\left[ {{{\left( {X - \mu } \right)}^5}} \right] = 0\end{array}\)

Therefore, the fifth central moment of X is 0.

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Most popular questions from this chapter

Suppose that X and Y are random variables such that

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