$X$ is a gaussian random variable with mean $\mu$, variance $\sigma^2$ .$Y=g(X)$ is also gaussianly distributed with mean $0$ and variance $1$ . Find $g(.)$
I can't figure out how i need to solve this. I' ve tried using Expected value and variance equation, i 've tried to go pdf from cdf. I might 've got little confused about $g(.)$ Can you help me please, thank you so much.
$Y = g(X) = X - \mu$ gives a Gaussian RV with a mean = ? Once you solve that, think about the transformation you can apply to normalize the variance (i.e. change the variance from $\sigma^2$ to $1$). Be careful to use the capital $X$ for $Y=g(X)$.