# Basic Notation Help

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.

Thanks

• Do you understand what $\{x\big\vert \vert x-1\vert\le 1\}$ means?
– Dave
Feb 26, 2022 at 20:32
• No that's where i'm struggling Feb 26, 2022 at 20:36
• 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.
– Dave
Feb 26, 2022 at 20:45
• 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. Feb 26, 2022 at 20:51
• 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 $\vert x-1\vert\le 1$.
– Dave
Feb 26, 2022 at 20:52

$$X$$ 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 $$0 \le X \le 2$$.