Recent content by Post-its

Thanks, I believe I figured it out!

Hi! I am also stuck on this question. Could we also show the set \overline{S}=\{(x_1,x_2):x_1^2+x_2^2\le 1\} is the closure of S=\{(x_1,x_2):x_1^2+x_2^2< 1\} by showing that (1) \overline{S} is closed, and (2) each point in \overline{S} is in the closure of S? To me, that would show that...

No! I am totally fine with assuming that B is rectangular. I'm just trying to decipher micro's post right now.

I like Serena: I haven't learned a formal way of dealing with infinitesimals, so I don't really understand that definition. I became very confused when I tried to think of the rationale for it. Karax: So if B is the region B=\{(x,y):x_{1} < x \le x_{2}, y_{1} < y \le y_{2}\}, then the...

I'd like to know how to prove (or show that it is reasonable) that the probability that a random vector (X, Y) assumes a value in the region B\subseteq \mathbb{R}^2 is (1) Pr((X, Y) \in B)=\iint\limits_B \, f_{X,Y}(x, y) \mathrm{d}x\,\mathrm{d}y. My textbook doesn't provide much of an...