suppose you sample from an urn with 12 red balls and 6 green balls. you choose 3 balls without replacement.

What is the Probability mass function for the number of red balls drawn? What is the mean, and the standard deviation for this distribution?

Let X be the number of red balls appearing in a draw of 3 balls from the urn.

The probability that exactly k balls of the n drawn are red is (the pmf):

Pr{X = k} = C(12, k) * C(6, 3-k) / C(18, 3)

The mean of the pmf (for the hypergeometric distribution) is, in this case, 3* (12/18).

The variance is V = 3 * (12/18) * (6/18) * [(18-3)/(17)], so the standard deviation s = sqrt(V)

BTW, C(a,b) is the number of combinations of a objects taken b at a time.

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