Taking a robotic planning class and have no stats background. I am just trying to understand what this means: "What is the probability of the event $R=\{x||x-1|\le 1\}$?"

Can someone tell me in plain words what the $R$ statement is saying? In the problem we are only given that mean$=1$, and variance$=1$. I read the whole chapter this question is based on and could not find a similar instance of this notation.


  • $\begingroup$ Do you understand what $\{x\big\vert \vert x-1\vert\le 1\}$ means? $\endgroup$
    – Dave
    Feb 26, 2022 at 20:32
  • $\begingroup$ No that's where i'm struggling $\endgroup$
    – kneesun
    Feb 26, 2022 at 20:36
  • $\begingroup$ Do you understand what $\vert x-1\vert\le 1$ means? // Perhaps part of the exercise is to learn how to interpret notation like this, but once you work through what it means, you’re going to see why I find this to be an obnoxious way for the assignment to write it. $\endgroup$
    – Dave
    Feb 26, 2022 at 20:45
  • $\begingroup$ i believe "abs value of x-1 is less than or equal to 1". I should have mentioned before that I have seen the vertical line used in conditional statements in probability functions, but I don't think this is a function so i'm not sure how to interpret it. $\endgroup$
    – kneesun
    Feb 26, 2022 at 20:51
  • $\begingroup$ It’s set notation. It means “the set of what’s left of the vertical bar such that right of the vertical bar is true”, so the set of all $x$ such that $\vert x-1\vert\le 1$. $\endgroup$
    – Dave
    Feb 26, 2022 at 20:52

1 Answer 1


$X$ is a random variable, the question is asking for what is the probability that event $R$ occur where $R$ is the event that $|X-1| \le 1$.

The condition is equivalent to $0 \le X \le 2$.

I don't think there is sufficient information unless you make more assumptions.


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