I am reposting a question on math.stackexchange which did not recieve good questions. The orginal questio is at http://math.stackexchange.com/questions/73091/distribution-of-a-maximum.

Randomly select $n$ numbers from ${\{1,2,\dots,m\}}$ without replacement, and order the chosen elements increasingly: $X_1 < X_2 < \dots < X_n$

And we can view each $X_i$ as a random variable, and we can get $\mathbb{E}(X_i) = \frac{(m+1)i}{n+1}$

And we can define $Y_i=|X_i-\mathbb{E}(X_i)|$ which is the distance of each variable to its corresponding expectation.

And we can also define $Z = \max_{1 \le i \le n} Y_i$

So what is the distribution of $Z$? And any bound of $Z$ is helpful.

I am reposting a question on math.stackexchange which did not recieve good questions. The orginal questio is at https://math.stackexchange.com/questions/73091/distribution-of-a-maximum.

Randomly select $n$ numbers from ${\{1,2,\dots,m\}}$ without replacement, and order the chosen elements increasingly: $X_1 < X_2 < \dots < X_n$

And we can view each $X_i$ as a random variable, and we can get $\mathbb{E}(X_i) = \frac{(m+1)i}{n+1}$

And we can define $Y_i=|X_i-\mathbb{E}(X_i)|$ which is the distance of each variable to its corresponding expectation.

And we can also define $Z = \max_{1 \le i \le n} Y_i$

So what is the distribution of $Z$? And any bound of $Z$ is helpful.