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Math Help - Stats first year help

  1. #1
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    Stats first year help

    Hello, i am preparing for my Statistics examination and would like to ask help with the questions i struggle.







    Am i right with these two?












    Would appreciate if You could help with any of these.
    Last edited by CaptainBlack; August 20th 2010 at 11:49 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by fancynick View Post
    Hello, i am preparing for my Statistics examination and would like to ask help with the questions i struggle.

    The pdf is:

    f(x)=\begin{cases}<br />
\theta e^{-\theta x}& , x>0\\<br />
0& , \text{otherwise}<br />
\end{cases}

    and the sketch looks OK

    CB

    ..
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by fancynick View Post


    \displaystyle E(x)=\int_{x=0}^{\infty} x\, \theta e^{-\theta x}\; dx

    so:

    \displaystyle E(x)=\left[-\dfrac{\left( \theta\,x+1\right) \,{e}^{-\theta\,x}}{\theta}\right]_{x=0}^{\infty}=\frac{1}{\theta}

    CB
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