problem 26

3.2.9 problem 26

If $X \sim HGeom (w, b, n)$ , then $n - X \sim HGeom (b, w, n)$ .

If $X$ counts the number of items sampled from the set of $w$ items in a sample of size $n$ , then $n - X$ counts the number of items from the set of $b$ items in the same sample.

To see this, notice that

P (n - X = k) = P (X = n - k) = \frac{(\frac{w}{n - k}) (\frac{b}{k})}{(\frac{w + b}{n})}

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