Some exercises have problems regarding direct use of the expected value. But one as follows asks to find the minimum expected value, how would I set the input values of integration for such a problem? Example.
Suppose $X$~$Exp(1)$. Find $E \ min (X,1)$
The general formula for the expected value of a continuous variable is $\int_{-\infty }^{\infty }xf(x)dx$ , but i can't see how to enter the values for the proper solution.
ps. Exp is the exponential distribution.
$$ E\min\{X,1\} = \int_{-\infty}^\infty \min\{x,1\} f(x) \, dx .$$ where $f(x)$ is the PDF.