I have a random variable $X$. The constants $a$, $b$ and $c$ are given. I have to find the interval $I$ such that $P(a\in (X-b,X+b))=c$. My question is actually not how to calculate this interval. How should I think of a random variable in an interval? Is there an intuitive way?
and $P((a-b)<X<(a+b))=F(a+b)-F(a-b)$ where F is the cumulative distribution function of random variable $X$