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Math Help - cumulative distribution function question

  1. #1
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    cumulative distribution function question

    consider rolling a die.
    S= {1,2,3,4,5,6}
    P(s)=1/6 for all s in S
    X= number on die so that X(s)=s for all s in S
    Y= X^2
    compute the cumulative distribution function Fy(y) = P(Y<=y), for all y in the set of real numbers.

    My guess
    for Y=1 i get
    P(-inf<y<=1)=P(Y<=1)-P(Y<-inf)=Fx(1)-Fx(-inf)
    = Fx(1)-0
    = Fx(1)

    Is this all I have to do for Y=1, or do I have to integrate, or is there anything wrong?
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  2. #2
    MHF Contributor harish21's Avatar
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    you have been told that  Y = X^2

    so,

     F_{Y}(y) = P(Y \leq y) = P(X^2 \leq y)

    continue further to find the cdf of Y....
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  3. #3
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    i go further but i am stuck at
    1-P(-x<y)-P(y<x)
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  4. #4
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    P(Y \leqslant x) = F_Y(x) = \left\{ {\begin{array}{rl}<br />
   {0,} & {x < 1}  \\<br />
   {\frac{1}<br />
{6},} & {1 \leqslant x < 4}  \\<br />
   {\frac{2}<br />
{6},} & {4 \leqslant x < 9}  \\<br />
   { \vdots ,} &  \vdots   \\<br />
   {1,} & {36 \leqslant x}  \\ \end{array} } \right.

    You fill in the blanks.
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  5. #5
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    ok i understand now.
    Last edited by mr fantastic; October 8th 2010 at 10:43 PM. Reason: Moved a new question to new thread.
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