# Expected value of the maximum of binomial random variables

Let $X = \{X_1, ..., X_k\}$ be a set of $k$ iid variables drawn from a binomial distribution: $X_i \sim B(n, p)$. How to calculate the upper bound of the expected value of $max(X_i)$?

Several related question (such as: Bounds for the maximum of binomial random variables or Maximum of Binomial Random Variables) give such estimates for cases when $n = k$. I am, however, interested in the general case.

• Careful - interesting and difficult questions posed by new users on this site are usually CLOSED down with facile remarks like: "What have you tried?" Then, they go off and answer homework questions ... ? – wolfies Jul 19 '17 at 17:08
