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Math Help - The cumulative distribution function

  1. #1
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    The cumulative distribution function

    Find the value of a and the value of b so that the following is a valid c.d.f.

    <br />
  F(x) = \begin{cases} 0, & \text { $x < 1$}, \\ \frac {1}{b}(2x^3 + ax - 2a), & \text {$1 \le x \le 3$}, \\ 1, & \text {$x > 3$}. \end{cases}

    -------------------
    So far I did,
    F(3) = 1/b (2x^3 + ax – 2a) = 1
    => 1/b(54+a)=1 ------------------(1)

    F(1) = 1/b (2x^3 + ax – 2a) = 0
    => 1/b (2-a) = 0 -----------------(2)

    From (1) & (2):
    a = 2 & b = 56.

    My book’s answers says: a = 2 & b =1/ 56.

    Is this method right? Where I did worng?
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  2. #2
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    Quote Originally Posted by geton View Post
    Find the value of a and the value of b so that the following is a valid c.d.f.

    <br />
F(x) = \begin{cases} 0, & \text { $x < 1$}, \\ \frac {1}{b}(2x^3 + ax - 2a), & \text {$1 \le x \le 3$}, \\ 1, & \text {$x > 3$}. \end{cases}

    -------------------
    So far I did,
    F(3) = 1/b (2x^3 + ax – 2a) = 1
    => 1/b(54+a)=1 ------------------(1)

    F(1) = 1/b (2x^3 + ax – 2a) = 0
    => 1/b (2-a) = 0 -----------------(2)

    From (1) & (2):
    a = 2 & b = 56.

    My book’s answers says: a = 2 & b =1/ 56.

    Is this method right? Where I did worng?
    You are correct, the book is wrong.
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  3. #3
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    hmmmmmmmmm I think so
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