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?

  • 1
    $\begingroup$ X = 10. And XII = 12. $\endgroup$ – wolfies Jan 17 '19 at 17:46
  • $\begingroup$ So it's like saying Y=X+2? $\endgroup$ – 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 $b$.


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