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Math Help - Density Functions

  1. #1
    Bar0n janvdl's Avatar
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    Density Functions

    Let F(x) = 1 - e^{- \alpha x^{\beta}} for x \geq 0 ; \alpha > 0 ; \beta > 0 ; and F(x) = 0 for x < 0.

    Show F is a cdf and find the corresponding density.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by janvdl View Post
    Let F(x) = 1 - e^{- \alpha x^{\beta}} for x \geq 0 ; \alpha > 0 ; \beta > 0 ; and F(x) = 0 for x < 0.

    Show F is a cdf and find the corresponding density.
    To show its a cdf you need to show that it is increasing, non-negative with a supremum of 1.

    Then since F is continuous and differentiable, the density is the derivative of F.

    RonL
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