# Tag Info

Accepted

### Independent random variables with $X^2 + Y^2 =1$

Example ... $X$ and $Y$ are independent, and both have the scaled Radermacher distribution $$P(X=1/\sqrt2) = P(X=-1/\sqrt2) = 1/2.$$ Then $X$ and $Y$ are not constant, they are independent, but ...
• 112k

• 14.2k
1 vote

### Independence assumption for interarrival time

You have to keep in mind the separation between a physical process and a model. We observe some process in the real world (customers arriving at a server) and want to construct a model that helps us ...
• 1,206
1 vote

### Independence of Sample Mean and Sample Variance

Yes it is a characterization for the normal distribution shown first by Geary (1936) that the sample mean and sample variance are independent if and only if the population distribution is normal. ...
• 7,270
1 vote

### Does Independence hold for $\sigma$-Algebras Generated by Disjoint Subsets of an independent Sequence

I think I understand how to prove it now. Please let me know, if my reasoning is correct. Big thanks to @IzzakvanDongen. Let $\mathcal{A}$ and $\mathcal{B}$ denote the sets of all possible finite ...
• 219

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