Just trying to get some properties straight. Was looking at a problem online which reads:
Let X be a random variable with mean μ and variance σ2. What is the variance of X/σ+10μ?
The solution of which is:
I assume this means $Var(X/σ+10μ)$ expands to $Var(X/σ)$ + $Var(10μ)$, then implying $Var(10μ)=0$.
Next, I assume $Var(X/σ)$ expands to $Var(X)/Var(σ)$, implying $Var(σ)=σ^2$.
Is this correct? Are these universal properties for all distributions? Or am I way off target?