- If $X$ and $Y$ are dependent random variables, then it is possible that $Var(X+Y) > Var(X) + Var(Y)$.
I only know that the two are equal for independent random variables; for dependent variables, would this be the case?
- According to forecasts, the end-of-year value in dollars of IBM stock has variance 10. If an investor holds a portfolio containing 5 shares of IBM stock and 240 dollars of idle cash, what is the variance in the end-of-year value in dollars of his portfolio?
I would assume it's 50, as variance is additive?
- If X and Y are random variables such that $P(X=0)=0.5$ and $P(Y=0)=0.1$, then is $P((X+Y)/2=0)$ equal to $P(X=0)/2 + P(Y=0)/2 = 0.3$?
I don't believe that it's possible to add probabilities like this, would I multiply instead?