Assume that X is a continuous and nonnegative random variable with the cumulative distribution function Fx. Let b > 0.
a) Find the cumulative distribution function of Y = XII{X ≤ b}.
b) Apply the general formula from (a) to exponential distribution with parameter λ > 0.
I'm having trouble understanding the notation for Y = XII{X ≤ b} What does "II" mean?
My guess is that $$ Y=XI(X\leq b)=\begin{cases} X&\text{if}\, X\leq b\\ 0& \text{if}\, X>b \end{cases} $$ so $Y$ equals $X$ truncated at $b$.