Introduction Statistics questions. I hope my question isn't too basic for this platform. I am given the CDF
I've found $P(X \leq 1)$. I've found $P(X > 1)$ by $1-P(X \leq 1)$.
Now I'm asked for $P(X\geq 1)$.
Is this the same as $P(X > 1)$? I know that $P(X=1)=0$ so does $P(X\geq 1)=P(X > 1)+P(X=1)$?
I'm also asked to find, $P(−1.5 < X < 0.5)$. I've previously only seen problems of the form $P(−1.5 < X \leq 0.5)$ and know to solve them by subtraction.
Intuitively, it seems that by including the possibility that $X=1$ would make $P(X\geq 1) > P(X > 1)$ but since $P(X=1)=0$, I suppose it doesn't.
For the purposes of my homework, how do I treat problems that are inclusive or exclusive of the number being asked about?
For my curiosity, there most be some difference in practice, right? $P(X\leq 1)$ would be close to $P(X\leq .99999999)$ which would be different than $P(x\leq 1)$. Or am I overthinking things?