# Lecture - Probability MT22, XV

### Flashcards

Are the basic formulas for discrete random variables like linearity of expectation, covariance, etc. also true for continuous random variables?

Yes.

What does it mean for continous random variables $X$ and $Y$ to be independent?:: If $f _ {X, Y} (x, y) = f _ X(x) f _ Y(y)$ for all $x$ and $y$.

How can you rewrite $F _ {X,Y}(x,y)$ for independent continuous random variables $x$ and $y$?

\[F_{X,Y}(x, y) = F_X(x) F_Y(y)\]

If $X$ and $Y$ are jointly normally distributed random variables, what does $\text{Cov}(X, Y) = 0$ imply (and why do you need to be careful)?

\[\text{Cov(X, Y)} = 0 \iff X, Y \text{ indep.}\]

Need to be careful since this equivalance fails in general.

When you two random variables whose domain are $(0, 1)$, then what do probabilities correspond to?

Areas.