Probability Mass Function

label Statistics
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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? 

Apr 27th, 2015

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)

Apr 27th, 2015

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

Apr 27th, 2015

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Apr 27th, 2015
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Apr 27th, 2015
Sep 24th, 2017
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