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Math Help - Help finding median

  1. #1
    Senior Member Danneedshelp's Avatar
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    Help finding median

    If Y had the density function

    f(y)=\left\{\begin{array}{cc}.2,&\mbox{ if }-1<y\leq 0\\ .2+1.2y,&\mbox{ if }0<y\leq 1\\0,&\mbox{ if }elsewhere\end{array}\right.

    Find the median and E[y-median].

    From what I have read, I need to solve \int_{-\infty}^{\infty}f(y)dy=\frac{1}{2}

    In this case, I have \int_{-1}^{m}\frac{1}{5}dy+\int_{m}^{1}\frac{1}{5}+\frac{  6}{5}ydy=\frac{1}{2}

    I end up with 0.91267

    Not sure that I am on the right track, some guidence would be great

    Thank you
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by Danneedshelp View Post
    If Y had the density function

    f(y)=\left\{\begin{array}{cc}.2,&\mbox{ if }-1<y\leq 0\\ .2+1.2y,&\mbox{ if }0<y\leq 1\\0,&\mbox{ if }elsewhere\end{array}\right.

    Find the median and E[y-median].

    From what I have read, I need to solve \int_{-\infty}^{\infty}f(y)dy=\frac{1}{2} Mr F says: No. Solve {\color{red}\int_{-\infty}^{m}f(y)dy=\frac{1}{2}}.

    In this case, I have \int_{-1}^{m}\frac{1}{5}dy+\int_{m}^{1}\frac{1}{5}+\frac{  6}{5}ydy=\frac{1}{2} Mr F says: No. Solve {\color{red}\int_{-1}^{0}\frac{1}{5} \, dy +\int_{0}^{m}\frac{1}{5}+\frac{6}{5}y \, dy = \frac{1}{2}}
    I end up with 0.91267

    Not sure that I am on the right track, some guidence would be great

    Thank you
    You should also sketch a graph of the pdf to see what's happening (it will be clear by the way that m > 0). It would then be clear that your answer looks much too big.

    For the next part note that E(Y - m) = E(Y) - m and you should know how to calculate E(Y) when given the pdf.
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