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 March 18th, 2018, 12:46 PM #1 Member   Joined: Feb 2018 From: Canada Posts: 46 Thanks: 2 The P.M.F. of Hypergeometric and Negative Binomial Distribution. A forest contains 100 deer. 20 of them have a red tag and 80 of them are untagged. A researcher samples 30 random deer without replacement. Let X be the number of tagged deer in the sample. From the sample of 30 deer, she will keep picking deer with replacement until she picks the fourth tagged deer. Let Y be the number of selections she makes until she gets her fourth tagged deer. Find the joint pmf of X and Y. This is my solution; can someone take a look for me? Thank you. Let X be the number of tagged deer in the sample of 30 random deer without replacement. $$X \sim \text{Hypergeometric(}N=100, n=30, r=20).$$ Let Y/X be the number of selections from the sample of 30 deer she makes until she gets her fourth tagged deer. $$Y/X \sim \text{Negative Binomial(}r=4, p=0.2).$$ The joint P.M.F. of X and Y is as follows: $$P_{X,Y}(x,y) = \begin{cases}0 &\text{if X=0 and Y is finite} \\ P(X=0)=\dfrac{\dbinom{20}{0}\dbinom{80}{30-0}}{\dbinom{100}{30}} &\text{if X=0 and Y is infinite} \\P_X(x)P_{Y/X}(y/x) = \dfrac{\dbinom{20}{x}\dbinom{80}{30-x}}{\dbinom{100}{30}} \dbinom{30-1}{4-1} 0.8^{30-4} 0.2^4 &\text{if }X=1,2,\dots ,20 \\ 0 &\text{ otherwise} \end{cases}$$ Last edited by skipjack; March 20th, 2018 at 04:22 PM. Tags binomial, distribution, hypergeometric, negative, pmf Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Anton29 Advanced Statistics 0 June 15th, 2012 03:59 AM hollymxox Probability and Statistics 1 April 19th, 2012 05:21 PM illusion419 Advanced Statistics 1 July 25th, 2011 06:40 PM WannaBe Advanced Statistics 0 May 3rd, 2010 12:55 AM damnpoop Advanced Statistics 0 October 31st, 2009 11:32 AM

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