wedtaur
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 Jan 4 comment Maximum load of a bin in the $n$ balls with weights into $m$ bins problem Perfect! There is a counterexample that prove that simple too? @Ofir Jan 4 comment Maximum load of a bin in the $n$ balls with weights into $m$ bins problem Ok, I've decomposed: $$E[max_i X_i]=E[max_iX_i|\text{"All X_i are equal"}]Pr[\text{"All X_i are equal"}]+E[max_iX_i|\text{"Not all X_i are equal"}]Pr[\text{"Not all X_i are equal"}]$$ Next I use the fact of $E[max_i X_i|\text{"Not all X_i are equal"}]>s$ to prove that: $$E[max_iX_i]>s$$ Am I right? Why that fact is true? Can you give me a counterexample to prove that? Jan 4 comment Maximum load of a bin in the $n$ balls with weights into $m$ bins problem @polkjh Sorry, but follow your idea in counterexample, why $E[X_i]=\frac1m\sum_{j=1}^{n} p_j$ is always true? Jan 4 awarded Scholar Jan 4 accepted Maximum load of a bin in the $n$ balls with weights into $m$ bins problem Jan 4 comment Maximum load of a bin in the $n$ balls with weights into $m$ bins problem Are you saying that $E[max_{1 \leq i \leq n} X_i]=E[X_i]$ for each $i$? Why? Jan 4 awarded Supporter Jan 4 comment Maximum load of a bin in the $n$ balls with weights into $m$ bins problem Thanks, I need some clarification: when you say $E[max_i X_i]=Prob[X_1=X...$, what concept do you use? Jan 4 awarded Editor Jan 4 revised Maximum load of a bin in the $n$ balls with weights into $m$ bins problem edited title Jan 4 awarded Student Jan 4 asked Maximum load of a bin in the $n$ balls with weights into $m$ bins problem