**"special treatment"**. So, if all fulfilled the criterion then we would expect $n$ subjects to receive the

**"special treatment"**. But we have observed that out of $n^2$ subjects $M$ patients do not fulfill the criterion hence receive no treatment.

The response times of the other $n^2-M$ subjects are known to us. We also know the lifetimes for $M$ non-responders. And it can happen that a subject dies before responding to the criterion. Now what should be the probability that the $i$-th subject gets the

**special treatment**?

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**The way I tried:**

**1)** First of all the probability of getting the **special treatment** for those who do not fulfill the criterion is $0$.

**2)** If we order the response times of the $n^2-M$ patients, then say the response times are $x_1<x_2<\ldots<x_i<\ldots<x_{n^2-M}$. So for $i$ to be the $k$-th smallest in a RSS block $(k-1)$ $x$'s should come before $x_i$ from the $x$'s. Let, among the $M$ non-responders, $M_i$ were observed to die before $x_i$ remitted. There can also be lowest $0$ to highest $m=min\{(n-k),M_i\}$ elements from these $M_i$ non-responders before $x_i$.

After $x_i$, there will be $(n-k-m)$ elements from the rest of $(n^2-i-M_i)$ elements.

I want to find out the probability that the $i$-th subject gets the **special treatment**.

Can anyone help please?