1
$\begingroup$

I am trying to prove two statistical formulas and I am having difficulties..

First, I am trying to prove the following:

If we have the random variable: $Y = \sum_{i=1}^n a_i X_i$

Prove that the variance of $Y$ is:

$$\operatorname{Var}(Y)=\sum_{i=1}^n a_i \operatorname{cov}(X_i,Y)$$

I later would like to do the same thing with $W$:

If we have the random variable: $$W = \sum_{i=1}^n b_i Y_i-c_i Z_i$$

Prove that the variance of W is:

$$\operatorname{Var}(W)=\sum_{i=1}^n b_i\operatorname{cov}(Y_i,W)-c_i\operatorname{cov}(Z_i,W)$$

Thank you!

$\endgroup$
  • $\begingroup$ Note that var(Y)=cov(Y,Y) and cov is bilinear. $\endgroup$ – Batman Oct 30 '16 at 22:32

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.