A random variable,uniform distribution

**Pringles** · January 6th 2009, 09:52 PM

A random variable is uniformly distributed over[0,1].What is its skew?

**Constatine11** · January 6th 2009, 10:28 PM

Originally Posted by Pringles

A random variable is uniformly distributed over[0,1].What is its skew?

[plagarism]

The skew of a RV X is:

$E\left( \frac{(x-\mu)^3}{\sigma^3}\right)=\frac{E( (x-\mu)^3)}{\sigma^3}$

where $\mu$ and $\sigma$ are the RV's mean and standard deviation.

Now for the uniform distribution on $[0,1]$

$p(x)=\begin{cases}1, & x \in [0,1]\\ 0, & \mbox{otherwise} \end{cases}$

and $\mu=1/2$

$\sigma=\sqrt{\int_0^1 (x-1/2)^2\ dx}$

(you may well know the value of the above, it's in most statistics books somewhere and engraved on the heart of everyone who has ever used Monte-Carlo methods in anger) and:

$E((x-1/2)^3)=\int_0^1 (x-1/2)^3\ dx$
[/plagarism]

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