
Order statistics
Hello
I'm working on the following problem but i am not quite sure what i should do or if this problem is solvable without a statistics program (eg. R):
Find out the smallest n so that $\displaystyle P(X_1<x_{0.5}<X_n) \geq 0.99$ whereas $\displaystyle X_1<X_2< \dots < X_n$ are order statistics of a sample n (of a continous distribution).
Can somebody help me?

is that x.5, the median?
In any case you will need the generic joint denisty of the smallest and largest order stats.
You seem to want the coverage to be .99.
So you will need to integrate that joint density and solve for when that probability exceeds .99