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## Homework Statement

You have an urn that contains n balls labeled with the natural numbers {1,2,3,...,n} and you extract n balls from the urn (with the condition that a ball may not be returned to the urn once drawn). You have to determine the distribution of X=(X

_{1},X

_{2},...,X

_{n}), where X

_{k}is the number of the ball from the k-th extraction.

## Homework Equations

For Z a discrete random variable, that can take the values 1, ..., n

Probability Distribution

p(z)=P(Z=z)

Cumulative Distribution Function

F(z)=P(Z<z)

where z is in {1,....,n}

## The Attempt at a Solution

There are n! possible cases.

X

_{k}(k={1,...,n}) are discrete random variable. Before the k-th extraction in the urn there are n-k+1 balls left with the probability of occurrence = 1/(n-k+1) and X

_{k}are discrete random variable:

1 2 ..... n

X_{1}: ( 1/n 1/n ...... 1/n )

considering i

_{1}the number of the ball extracted on the first extraction, we have:

1 ... i

X_{1}-1 i_{1}i_{1}+1 .. n_{2}: ( 1/(n-1) ... 1/(n-1) 0 1/(n-1) .. 1/(n-1) )

that means that for i

_{1}the probability of occurrence = 0.

....

before the last extraction there is 1 ball left in urn, that obviously, has the probability of occurrence = 1.

I have no clue what to do next and I need it to demonstrate something for a bigger project. I do not ask you for the solution, I just need some hints.

P.S.: I hope you will understand what I wrote here, I've tried my best. Sorry if you don't, english is not my native language.