# How to find PDF and Expected value of max(x,0), for a random variable x

• MHB
user_01
Let $a,b,c, \tau$ be positive constants and $x$ is an exponentially distributed variable with parameter $\lambda = 1$, i.e. $x\sim\exp(1)$.

E = \tau\Big[a\frac{1+a}{1+e^{-bx+c}} - 1 \Big]^+

where $[z]^+ = \max(z,0)$

How can I find

1. The PDF for $E$
2. The expected value of E.