# Thread: Formulas for dependent RV's

1. ## Formulas for dependent RV's

$X$ and $Y$ are random variables with standard deviation $\sigma_X=0.2$ and $\sigma_Y=0.2$. They are both distributed normally, with $\mu_X=\mu_Y=0$ and correlation $\rho_{XY}=-0.2$ (they are not independent).

(a) Find the standard deviations of 3X.

Is this just 3(0.2) = 0.6?

(b) Find the standard deviation of X - Y

How do I do this is X and Y are not independent? What is the formula for dependent RVs?

(C) What is $P(|X-Y|>1)?$

Thank you.

2. (a) is fine

(b) $V(X-Y)=V(X)+V(Y)-2Cov(X,Y)$.

Where the correlation equals ${Cov(X,Y)\over \sigma_x\sigma_y}$.

So, $Cov(X,Y)=(.2)(.2)(-.2)$.

(c) Here you need to standardize $X-Y$, by subtracting off its mean, which clearly is 0 and dividing by it's standard deviation.