- #1
user_01
- 8
- 0
Let $a,b,c, \tau$ be positive constants and $x$ is an exponentially distributed variable with parameter $\lambda = 1$, i.e. $x\sim\exp(1)$.
\begin{equation}
E = \tau\Big[a\frac{1+a}{1+e^{-bx+c}} - 1 \Big]^+
\end{equation}
where $[z]^+ = \max(z,0)$
How can I find
\begin{equation}
E = \tau\Big[a\frac{1+a}{1+e^{-bx+c}} - 1 \Big]^+
\end{equation}
where $[z]^+ = \max(z,0)$
How can I find
- The PDF for $E$
- The expected value of E.