Question

If FX (x)=[1-e^(-αx) ]U(x-c)). Find fx (x ).

Answer 1

Answer on Question #48729 – Math – Statistics and Probability

If $F_{X}(x) = [1 - e^{-\alpha x}]U(x - c)$. Find $f_{X}(x)$.

Solution

$$U(x - c) = \begin{cases} 1, & \text{if } x > c \\ 0, & \text{if } x < c \end{cases}$$ $$f_{X}(x) = \frac{\partial F_{X}(x)}{\partial x} = \frac{d}{dx} [1 - e^{-\alpha x}] \cdot U(x - c) = -\alpha \cdot (-e^{-\alpha x}) U(x - c) = (\alpha e^{-\alpha x}) U(x - c).$$

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