Suppose that X is a random variable with mean 17 and standard deviation 5. Also suppose that Y is a random variable with mean 45 and standard deviation 11. Find the variance and standard deviation of the random variable for the following case:
Z= 4 + 9X
I just need to know the process of finding it. Thanks!
If $a$ and $b$ are constants, then for a random variable $X$, $$Var(a+bX)=b^2Var(X)$$ So here $$Var(Z)=Var(4+9X)=9^2Var(X)$$ And you already know $Var(X)$ from your given information, since the standard deviation is the square root of variance.