Imagine you sample $n$ number with replacement uniformly from the integers $1,\dots, n$. Let $X$ be the minimum of these samples. I am interested in $\mathbb{E}(X)$ but with a twist. All I know is that the samples are uniform and pairwise independent.

Assuming $n$ is large, what bounds can one get for $\mathbb{E}(X)$?

If we generalize this to $k$-wise independence, for $k \geq 2$, what can we say?

[Also asked at http://math.stackexchange.com/questions/1179943/expected-value-of-the-minimum-with-limited-independence previously. ]

Imagine you sample $n$ number with replacement uniformly from the integers $1,\dots, n$. Let $X$ be the minimum of these samples. I am interested in $\mathbb{E}(X)$ but with a twist. All I know is that the samples are uniform and pairwise independent.

Assuming $n$ is large, what bounds can one get for $\mathbb{E}(X)$?

If we generalize this to $k$-wise independence, for $k \geq 2$, what can we say?

[Also asked at https://math.stackexchange.com/questions/1179943/expected-value-of-the-minimum-with-limited-independence previously. ]

Imagine you sample $n$ number with replacement uniformly from the integers $1,\dots, n$. Let $X$ be the minimum of these samples. I am interested in $\mathbb{E}(X)$ but with a twist. All I know is that the samples are uniform and pairwise independent.

Assuming $n$ is large, what bounds can one get for $\mathbb{E}(X)$?

If we generalize this to $k$-wise independence, for $k \geq 2$, what can we say?

[Also asked (by a friend) at http://math.stackexchange.com/questions/1179943/expected-value-of-the-minimum-with-limited-independence previously. ]

Imagine you sample $n$ number with replacement uniformly from the integers $1,\dots, n$. Let $X$ be the minimum of these samples. I am interested in $\mathbb{E}(X)$ but with a twist. All I know is that the samples are uniform and pairwise independent.

Assuming $n$ is large, what bounds can one get for $\mathbb{E}(X)$?

If we generalize this to $k$-wise independence, for $k \geq 2$, what can we say?

[Also asked at http://math.stackexchange.com/questions/1179943/expected-value-of-the-minimum-with-limited-independence previously. ]