Dingo13
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 Apr17 asked How simplify this sum? Sep25 comment Curiosity - maximising a product with a constraint Thanks for your help. Sep25 comment Curiosity - maximising a product with a constraint Does your hint allow to show that " In general, you can show that a product of several numbers (with constant sum) get maximised when they can be made as close to each other as possible" ? Sep25 comment Curiosity - maximising a product with a constraint Thanks. Why do you say that $i_3-1 \geq i_4$ ? The $i_j$s are in descending order but not strict, we can have $i_3=i_4$. Sep25 comment Curiosity - maximising a product with a constraint Yes I understand when there si only one substraction, but what about the case where $c=3$ and we substract $1$ to $i_2$, substract $1$ to $i_3$ and substract $1$ to $i_4$. There are a lot of other possibilities. Sep25 comment Curiosity - maximising a product with a constraint Thanks. As you say at the end, in fact we can have also the possibility to substract $1$ to $i_2$, $1$ to $i_3$, ..., $1$ to i_{c+1}. Such a possibility lets the sum unchanged. There are again a lot of other possibilities. Sep25 comment Curiosity - maximising a product with a constraint Thank you for the hint. Sep25 comment Curiosity - maximising a product with a constraint Exact. Thank you :-). Sep25 revised Curiosity - maximising a product with a constraint edited body Sep25 comment Curiosity - maximising a product with a constraint I've changed a little the post for better understanding. Sep25 revised Curiosity - maximising a product with a constraint added 104 characters in body Sep25 comment Curiosity - maximising a product with a constraint @Paul If we want to add $2$ to $i_1$, we have to substract $2$ to $i_2$ so that the sum is unchanged and the product is maximised. Sep25 asked Curiosity - maximising a product with a constraint May2 comment Average number of distinct values OK. Thanks again André May2 comment Average number of distinct values I have a question André. You write "For $E(X_i)$, the probability that $X=i$". Is there a typing error ? $X$ is not defined. May2 comment Average number of distinct values Thank you very much André. May2 revised Average number of distinct values added 27 characters in body May2 comment Average number of distinct values Thanks Did. In fact $q$ is lower than $n$. I update my question. May2 asked Average number of distinct values Oct18 revised Curiosity in a product deleted 72 characters in body