# X is a normal random variable and Y=g(X) , Y is standart normal random variable

$$X$$ 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.

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

## 1 Answer

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

• 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) – Ahmet Yusuf Yahşi Apr 4 at 19:40
• Try drawing the distributions as pictures on paper to understand where the motivation for the initial transformation comes from. – Eric Apr 4 at 20:08
• Okay, i 'll try to do it. Thank you again :D – Ahmet Yusuf Yahşi Apr 4 at 20:12