Let F(x) = 1 - e^{- \alpha x^{\beta}} for $\displaystyle x \geq 0$ ; $\displaystyle \alpha > 0$ ; \beta > 0 ; and $\displaystyle F(x) = 0$ for $\displaystyle x < 0$. Show F is a cdf and find the corresponding density.
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Originally Posted by janvdl Let F(x) = 1 - e^{- \alpha x^{\beta}} for $\displaystyle x \geq 0$ ; $\displaystyle \alpha > 0$ ; \beta > 0 ; and $\displaystyle F(x) = 0$ for $\displaystyle x < 0$. 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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