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Thread: Combination or Permutation

  1. #16
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    Re: Combination or Permutation




    Quote Originally Posted by BGM View Post
    \Pr\{X = x, Y = y\} = \frac {\displaystyle \binom {2} {x} \binom {7} {y}} {\displaystyle \binom {9} {3}} = \frac {\displaystyle \binom {2} {x} \binom {7} {3-x}} {\displaystyle \binom {9} {3}} = \Pr\{X = x\}
    Does this formula consider both variables already (Ie., the probability of X and Y together)?

  2. #17
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    Re: Combination or Permutation

    I guided myself with this one http://bit.ly/vtozxA. But that doesn't guide me how to get the probabilities of BOTH X and Y occurring. I have to compute separately for X and Y using the given formula in that site. And to get their joints, I had to multiply the separate probabilities computed which you said is not appropriate. Please tell me how do we get the probabilities when both occur together (ie. X=2 and Y=1; Y=2 and X=1). Getting P(X and Y) is a joint probability and that's what I need. The correlation is given in this problem and it is -1. When I tried to compute for the correlation, it does not equal to -1 so I concluded that indeed what I did was wrong.

  3. #18
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    Re: Combination or Permutation

    First, you should know that X = 2 if and only if Y = 1.

    So both events are equivalent, and therefore

    \Pr\{X = 2\} = \Pr\{X = 2 ~~\text{and}~~ Y = 1\} = \Pr\{Y = 1\}

    The formula I given to you is usually known as the probability mass function of an univariate hypergeometric distribution (that is the usual notion).
    Please do not think it is a two dimensional problem - it is a univariate problem as I have emphasized several times already.

    So anyway you should know that the support of (X, Y) is \{(0, 3), (1, 2), (2, 1)\} and evaluate the pmf at these points

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    dEconomist (12-31-2011)

  5. #19
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    Re: Combination or Permutation

    Your formula is different from my readings. Yes, I know that X+Y=3. Why there are two rows inside the parentheses? What is the operation to be used for that? Is that equivalent to (kCx)(N-kCn-x) all over by NCn? The variables before and after C here are subscripts.

  6. #20
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    Re: Combination or Permutation

    And I know a bit of multinomial but isn't that for with repetition only?

  7. #21
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    Re: Combination or Permutation

    I think I get it. The probabilities obtained using the hypergeometric distribution is good as the joint probability already. Say, we get P(X=0), using hypergeometric, it is 5/12, then that means we actually obtain 3 of Ys. And when P(Y=2), that is 1/2, then that means there is one of X.

  8. #22
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    Re: Combination or Permutation


    Yes I think you have got it.

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