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    basic problem computing pdf




    If I have a pdf, say X~Uniform[-3,3] and Y= -X, would the pdf of Y be 1/6 [-3,3] ? How would I get the pdf using P(-X < - y) = P(X > y) = 1 - P( X < y) = 1- integral 1/6 from -3,3 so differentiating to get pdf we get -1/6 for [-3,3] but the pdf is negative so I assume my assumption Y is 1/6 is right. Where did I make my mistake?

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    Re: basic problem computing pdf

    Ok suppose you are first computing the CDF:

    For y \in [-3, 3],

    F_Y(y) = \Pr\{Y \leq y\} = \Pr\{-X \leq y\} = \Pr\{X \geq -y\}

    (Note that -y \in [-3, 3] so the following integral hold)

    = \int_{-y}^3 \frac {1} {6} dx  = \frac {y + 3} {6}

    Therefore by differentiation you obtain the desired answer.

    Outside this range the CDF of Y is constant (0 or 1) so [-3, 3] is the support of Y

  3. The Following User Says Thank You to BGM For This Useful Post:

    stephanie (11-29-2013)

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    Re: basic problem computing pdf


    Thank you this really helped me

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