$X$ 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.

  • $\begingroup$ Thank you for showing me how to, i did it now :D $\endgroup$ – Ahmet Yusuf Yahşi Apr 6 at 3:29

$Y = g(X) = X - \mu$ 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 $Y=g(X)$.

  • $\begingroup$ Thank you so much for explanation i will try that and i 've edited for Y=g(X) , but where is this come from X−μ = g(X) $\endgroup$ – Ahmet Yusuf Yahşi Apr 4 at 19:40
  • $\begingroup$ Try drawing the distributions as pictures on paper to understand where the motivation for the initial transformation comes from. $\endgroup$ – Eric Apr 4 at 20:08
  • $\begingroup$ Okay, i 'll try to do it. Thank you again :D $\endgroup$ – Ahmet Yusuf Yahşi Apr 4 at 20:12

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