Question

suppose X has amean of 5 and standard deviation of 2, what are the mean and standard deviation of ((3x)+4)​

Answer 1

If you apply a linear transformation

$aX+b$

to a random variable X, the mean and standard deviations change as follows:

$\mathbb{E}(aX+b)=a\mathbb{E}(X)+b$

$\sigma(aX+b)=a\sigma(X)$

So, the new mean is

$3\cdot 5+4=15+4=19$

and the new standard deviation is

$3\cdot 2=6$