Statistics - "within" keyword

Say you had the following:

X = # of hours past midday
F(X) = x, 0 <= x < 24

If you wanted to calculate if the random variable would be within 3 hours would it be P(X < 3) or P(X <= 3)?

P(X<=3), IMO.

Edit Changed my mind.

Consider what within 1 hour means. Would F(x) by 0 or 1?

Say you had the following:

X = # of hours past midday
F(X) = x, 0 <= x < 24

If you wanted to calculate if the random variable would be within 3 hours would it be P(X < 3) or P(X <= 3)?

Within, to me, implies under 1 hour (i.e. < not <=).

Just wanted to check if I was correct

< was my initial thought.

It looks to be a discrete uniform distribution.

Then I though about what the r.v. represented, or might represent, since there's no info there, and decided <=. But could be either I suspect.

Is there any background information?

Im confused :/ generally within 1 hour means including 1 hour?

If it said continuous uniform F(X < 3) would be the same as F(X <= 3), yes?

The keyword threw me as I was doing the problem and there isn't any background information other than what I posted.




I'm really not sure.

Logically thinking I assumed it wasn't including 1 hour but I may be wrong.

Yes.

What about F(X) = x, 0 <= x < 24 ?

If this is meant to be the cumulative distribution, then it should have a max value of 1, not 23.

I have interpreted this as a discrete distribution, but is it?