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 Nov6 awarded Popular Question Nov5 asked Can Cauchy Schwarz inequality be proven using Jensen's inequality? Nov5 revised Writing clear proofs involving multiple theorems and conditions added 45 characters in body Nov5 asked Writing clear proofs involving multiple theorems and conditions Nov5 accepted Are two random vectors independent, iff every pair of components from each vector are independent? Nov5 accepted Independence and uncorrelatedness between two normal random vectors. Nov5 comment Normal random Vector Thanks. +1............... Nov5 comment Does a Pareto distribution always have variance? There is no such thing called "forever". Nov5 asked If $X < a$, $EX < a$? Nov5 comment Does a Pareto distribution always have variance? Thanks, @Committingtoachallenge Nov5 awarded Popular Question Nov4 comment Does a Pareto distribution always have variance? I think Wikipedia is using a different definition: $Var X := EX^2 - (EX)^2$, which is why it says the variance doesn't exist when $EX$ is infinite. @Did. Nov4 comment Independence and uncorrelatedness between two normal random vectors. Yes, there is such a theorem, i.e. mean and variance do characterize multivariate normal distribution completely. Why? and how to think about $var([X,Y])$? Nov4 comment Independence and uncorrelatedness between two normal random vectors. Yes. it is defined that way. @MichaelHardy Nov4 comment Independence and uncorrelatedness between two normal random vectors. @MichaelHardy: It is what I think and guess out of my old notes, not an exercise. So I am not claiming my phrasing is correct. Yes, the emphasis is from 1 to 2. Nov4 asked Independence and uncorrelatedness between two normal random vectors. Nov4 comment Does a Pareto distribution always have variance? As you mentioned in your comment to my linked reply, the Wikipedia article in question uses "the one that makes a random variable with infinite expectation have undefined variance". But I don't think it is the most standard one, and I am not alone. Nov4 asked Are two random vectors independent, iff every pair of components from each vector are independent? Nov4 comment Does a Pareto distribution always have variance? Kevin, Thanks. I realized something, something why Wikipedia wrote about the Parento distrn that way, although I still think you claim that the two are the same is wrong. Nov4 comment Does a Pareto distribution always have variance? I pointed out that they are not, in my last comment and here math.stackexchange.com/questions/1004772/…. I am happy if you can convince me otherwise.