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.