# Find the cumulative distribution function of Y = XII{X ≤ b}.

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?

• X = 10. And XII = 12. – wolfies Jan 17 '19 at 17:46
• So it's like saying Y=X+2? – Slam95 Jan 17 '19 at 18:02

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 $$b$$.