It's a geometric distribution but suppose we didn't know that
ELI5 Please
BCom acct/fins @UNSW
Quick question regarding probability spaces:
leehuan - what would you do if InteGrand decides to take a 6 month sabbatical?
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Last edited by Drongoski; 6 Mar 2017 at 2:00 PM.
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I wasn't taught the hypergeometric distribution properly so can someone walk me through how to use it? Here's my question if it helps to refer to it.
A factory produces 80 items in a batch. To test if the batch is defective, an acceptance sampling scheme is adopted: a random sample of 10 items is selected, and if 2 or more items don’t meet customer specifications, the batch is considered defective.
If there are actually 11 defective items in the batch,
1i) What is the probability that 2 sampled items are defective?
ii) What is a general formula for x sampled items being defective?
Doing this for the first time for a very very long long time. Not sure if correct.
Last edited by Drongoski; 21 Mar 2017 at 2:25 PM.
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The parameters are as follows:
• N is the total population
• K is the number of "tagged" objects (defective objects in your example)
• n is the size of our sample.
The hypergeometric distribution pmf Drongoski wrote (in terms of the parameters N, K, n) then gives the probability that our sample has exactly k "tagged" (defective) objects present, under the assumption that we are sampling without replacement. This follows from basic combinatorics.
The reason for terms like "population" and "tagged" is that one place this distribution comes up is in ecology when we tag some members of an animal population (like a fish population) and then later draw (without replacement) a random sample from the animal population and count how many are tagged. This can be used to try and estimate the total population for example (it is sometimes known as the "capture-recapture method", and you can read more about it here: https://en.wikipedia.org/wiki/Mark_and_recapture).
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