# Math Help - Density Functions

1. ## 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.

2. Originally Posted by janvdl
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