# What is the standard deviation of multiple correlated random variables subtracted from another random variable?

Wiki states that standard deviation of $X-Y$ is:

$$\sigma_{x-y} = \sqrt { \sigma_x^2 + \sigma_y^2 - 2\rho\sigma_x\sigma_y }$$

I have a number (say 3) correlated random variables to be subtracted from another correlated random variable.

All random variables have identical correlation $\rho$.

Can I subtract each one in turn like this:

$$\sigma_{x-1} = \sqrt { \sigma_x^2 + \sigma_1^2 - 2\rho\sigma_x\sigma_1 }$$

$$\sigma_{x-2} = \sqrt { \sigma_{x-1}^2 + \sigma_2^2 - 2\rho\sigma_{x-1}\sigma_2 }$$

$$\sigma_{x-3} = \sqrt { \sigma_{x-2}^2 + \sigma_3^2 - 2\rho\sigma_{x-2}\sigma_3 }$$

The application is determining carrier-to-interference ratio of multiple co-channel interferers in an environment where it can be assumed that each interferer has identical correlated variation.

-
