What are the key differences between discrete and continuous PMFs?

[RJLiberator]

Homework Statement

Let P_{x}(x) = \frac{x}{15}, x = 1,2,3,4,5 ; 0 elsewhere
be the pmf of X. Find P(X=1 or 2), P(1/2 < X < 5/2), P(1 ≤X≤2).

Homework Equations

The Attempt at a Solution

I believe what this problem is trying to show is the difference between discrete and continuous Pmf functions.

First, I believe the answer to ALL three parts is 3/15 as this is a discrete interval for x.
However, what is throwing me off is the continuous intervals in P(x).

Let me explain my answers:
1) If X = 1 or 2 then this is the easy solution of 1/15+2/15.
2) if we have the interval 1/2 < x < 5/2 well, the only x values that matter are still x = 1 or x = 2. Same answer.
3) Similarly, we have 1 and 2 included, so 3/15.

Am I doing anything wrong here? Is my thinking correct?

Thank you.

 

[Stephen Tashi]

Is my thinking correct?

You have the correct answers. Your thinking is correct - unless you are taking a very advanced course that expects you to derive the answers using generalized definitions of integration.

 

[RJLiberator]

Perfect, thank you much for the confirmation.
I just didn't want it to end up being a trick question considering all three parts have the same answer. So the question just wanted to clarify discrete vs. continuous after all.

Cheers.