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`