Hey all I'm having a hard time finding the right intuition (and formula) for this problem:
X and Y are independent random variables. X is normally distributed
with mean 1 and variance 1. Y is normally distributed with mean 3 and
variance 5. What is the variance of Y-2X?
I thought that if the variables are independent, the Covariance is zero and the Variance of the sum or the difference is the same, i.e. Var(X + Y) = Var(X-Y) = Var(X) + Var(Y). But I'm not sure if that applies here. Any help is much appreciated!
Best Answer
The generalisation $\operatorname{Var}(aX+bY)=a^2\operatorname{Var}X+b^2\operatorname{Var}Y$ is what you need. In this case, we get $(-2)^21+1^25=9$.