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seen Jan 10 '13 at 0:03

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