Thread: A random variable,uniform distribution
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Old January 7th, 2009, 12:28 AM
Constatine11 Constatine11 is offline
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Quote:
Originally Posted by Pringles View Post
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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Last edited by Constatine11; January 7th, 2009 at 03:55 AM. Reason: replace reference by outright theft of someone else's text
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