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### Distribution of function of variable having a Gaussian distribution

If I have a variable $X$ whose Gaussian distribution is known and let $f$ be a known function, is there a way to compute the distribution of $f(X)$ i.e. the resulting Gaussian distribution from this? ...
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### Sum of Gaussian is Gaussian?

As a newbie in probability, I am recently cleaning my understandings about Gaussian distribution. I know that If $X$ and $Y$ are jointly Gaussian, then $aX+bY$ ($a$ and $b$ are both constant) is ...
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### Data transformation using copulas

I've heard about the use of copulas to transform data. For instance, supposedly it's applied to data that is non-normal to make it look more normal. However, I don't quite understand how this is done. ...
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### Does uncorrelation imply independence for marginally Gaussian random variables?

Let $X_1, \ldots, X_n$ be marginally Gaussian distributed random variables that are uncorrelated. Does it imply that they are independent?
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### Python: Gaussian Copula or inverse of cdf

Let's say I have a column x with uniform distributed values. To these values, I applied a cdf-function. Now I want to calculate the Gaussian Copula, but I can't find the function in python. I read ...
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### How to change exponential distribution into Normal distribution? [closed]

We have random data, which is exponentially distributed. Data = exp($\lambda$), where $\lambda$ = 0.5. If it is possible to change exponential distribution into the normal distribution. Then what ...
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### How to transform an arcsine distribution to a normal distribution?

I have a distribution that looks like this: U In other words small and big values are more frequent than middle values. A better graphical example of the distribution is this: Here So I have a ...
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### Is it possible for $X$ and $Y$ to be marginally normally distributed and have $E[Y|X]$ be a nonlinear function of $X$? [duplicate]

Is this at all possible? What is the intuition for this?
I have this doubt: Consider $X$~$N(\mu_X,\sigma^2)$, $Y$~$N(\mu_Y,\sigma^2)$ and $Z=X-Y$ I know that $E(Z)=E(X)-E(Y)=\mu_X-\mu_Y$ because the expected value is a linear operator. And I know that \$...