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Find the probability function $f(x) = P(X = x)$

I have a few questions,

I could try to find $F(x) = P(X \le x)$, but I don't understand how to do this conceptually.

So the way I see it,

$A = \text{Range } X$ depends on how many balls are picked.

So what is a way to approach this? Can you also provide some conceptual understanding?

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    Hint : $P(X\leq x)=$ probability that all balls are $\leq x$... – 2017-01-27
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    Can you say how do you understand the definition of $X$ ? For me the definition is a little bit too vague. – 2017-01-27
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    $$P(X=x)=\frac{{x\choose n}-{x-1\choose n}}{{N\choose n}}$$ – 2017-01-27

1 Answers 1

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For $X$, the largest number selected among $n$ balls, to be $x$, you must select ball numbered $x$, and $n-1$ from the $x-1$ balls which have smaller numbers.   The probability of doing this is what you seek.

Since you are selecting without replacement, $x$ cannot be smaller than $n$; giving you the support interval of $X\in\{n,\ldots, N\}$