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Math Help - continuous random variables

  1. #1
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    continuous random variables

    A continuous random variable Y has cdf

    F(y) = a + ay / 2, − 2 < y < 0
    1− becy 3 , y > 0
    (a)
    Sketch the cdf when a = 1/2, b = 1/2 and c = 1.
    Then derive Y's pdf generally, and sketch it when a = 1/2, b = 1/2 and c = 1.
    Finally, write down the range of possible values for a, b and c.

    (b) Find P(Y > −1| Y < 1) when a = 1/2, b = 1/2 and c = 1.
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  2. #2
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    Quote Originally Posted by Mathew View Post
    A continuous random variable Y has cdf


    F(y) = a + ay / 2, − 2 < y < 0
    1− becy 3 , y > 0 Mr F says: The formatting of this is horrible. I can't understand it.


    (a)
    Sketch the cdf when a = 1/2, b = 1/2 and c = 1.
    Then derive Y's pdf generally, and sketch it when a = 1/2, b = 1/2 and c = 1.
    Finally, write down the range of possible values for a, b and c.


    (b) Find P(Y > −1| Y < 1) when a = 1/2, b = 1/2 and c = 1.

    Where are you stuck? Note:

    (a) Differentiate the cdf to get the pdf.

    (b) \Pr(Y > -1 | Y < 1) = \frac{\Pr(-1 < Y < 1)}{\Pr(Y < 1)} = \frac{F(1) - F(-1)}{F(1)}.

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