So, I'm trying to get my head around a question and I was wondering if you could help me.
Given that the correlation coefficient $\rho$ for random variables $X$ and $Y$ is: $\;\rho_{\lower{0.5ex}{X,Y}} = \mathsf E[X^\ast\,Y^\ast]$
Where $X^\ast$ and $Y^\ast$ are the standardised versions of random variables $X$ and $Y$ respectively. And given that $a$ is an unknown coefficient
What is the numerical value of $\rho_{\lower{0.5ex}{X,Y}}$ if $X = aY + b$?
Hint: If $X=aY+b$ then how are $X^*$ and $Y^*$ related?