I have 2 variables, which I can't be sure to call them random variables. They are aggregates from multiple measurements of two distinct phenomena. I don't have access to the raw measurements data, just the aggregates: Var A with mean $\mu_1$ and standard deviation $\sigma_1$, and Var B with mean $\mu_2$ and standard deviation $\sigma_2$.
I want to calculate Var C which given by the following formula:
I'd imagine for Var C's mean $\mu_3$, this boils down to
How about Var C's standard deviation $\sigma_3$? Is it even possible to calculate Var C mean and standard deviation given only the means and standard deviations for Var A and B?