Consider the following problem. a, b are constants in [0,1] and x is a random variable drawn from a continuous distribution F with support on [0,1]. Let $1_m$ represent the indicator function associated to the event m.
I want to calculate the following:
$E_x [(a-x) 1_{(b<x<a)}]$
Which I believe is of the form:
$\int_b^a (a- x) f(x)$ $dx$
But I do not know if this is true or how to get the solution. Any help is deeply appreciated. Thanks,