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The normal, or Gaussian, distribution has a density function that is a symmetrical bell-shaped curve. It is one of the most important distributions in statistics. Use the [normality-assumption] tag for asking about testing for normality.

3 votes
2 answers
176 views

What is $E\left[\frac{X^2}{X^2+Y^2}\right]$ if $X$ and $Y$ are normally distributed but not ...

I assume that X and Y are normally distributed with individual mean and variance. So far, I have found that an analytic expression exists for $E[X^2+Y^2]$, $E[X^2*Y^2]$ and $E[X^2*(X^2+Y^2)]$, all usi …
Jannis's user avatar
  • 362
1 vote
1 answer
71 views

What is the correct Gaussian to use given that I know the true second moment and have one sa...

I have some random variable $X$ that is normal distributed. I know the second moment $s = \mathbb{E}[X^2]$ and have one sample x from the distribution. How can I get an unbiased estimate of the mean a …
Jannis's user avatar
  • 362
0 votes

What is the correct Gaussian to use given that I know the true second moment and have one sa...

So I have figured out a partial answer to my question: I think it would be good to approach this from a Bayesian perspective where we have a prior over normal distributions given the second moment and …
Jannis's user avatar
  • 362