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Math Help - Probability Density Function

  1. #1
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    Probability Density Function

    Suppose that a random variable Y has a probability density function given by

    f(y) = {6y(1-y), 0 <= y <= 1 AND 0 elsewhere}

    a)Find F(y)
    b)Graph F(y) and f(y)
    c)Find P(.5<=Y<=.8)

    Thanks for any help!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jzellt View Post
    Suppose that a random variable Y has a probability density function given by

    f(y) = {6y(1-y), 0 <= y <= 1 AND 0 elsewhere}

    a)Find F(y)
    b)Graph F(y) and f(y)
    c)Find P(.5<=Y<=.8)

    Thanks for any help!!
    Let's start with a).

    \displaystyle F_Y(y)=\int_{-\infty}^y f_Y(\zeta)d\zeta

    where:

    f_Y(y)=\left\{ \begin{array}{ll}6y(1-y),& 0 \le y \le 1 \\  \\ 0, & \text{otherwise}\end{array} \right.

    Now what exactly is the problem you are having with this?

    CB
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  3. #3
    MHF Contributor matheagle's Avatar
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    This is a \beta(2,2) by the way.

    That's why the \Gamma(4)=6 is your coefficient.
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