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Thread: A random variable,uniform distribution

  1. #1
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    A random variable,uniform distribution

    A random variable is uniformly distributed over[0,1].What is its skew?
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  2. #2
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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:

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

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

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

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

    and $\displaystyle \mu=1/2$

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

    (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:

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


    .
    Last edited by Constatine11; Jan 7th 2009 at 01:55 AM. Reason: replace reference by outright theft of someone else's text
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