Normal and standard distribution question

I have [tex] X \sim N(0,1)[/tex]
and [tex] Y \sim N(\mu,\sigma^2)[/tex]

Apparently then [tex] Y =\sigma X[/tex] + [tex]\mu[/tex]

I can't quite see how, and can't find anything on the web. Can someone point me in the right direction?


TS Contributor
If you have the first two conditions given, then you can conclude that

\( Y \) and \( \sigma X + \mu \)

has the same distribution, which is slightly differ from the third condition.

On the other hand, if the third condition is given, then given any one of the first two condition, we can conclude the other condition hold.

The location-scale transformation is quite standard here. In multivariate case, see e.g.


Ambassador to the humans
aroko89 if you don't make your own thread I will have to ban you for spamming other threads with unrelated questions.