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Math Help - joint probability mass function

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    joint probability mass function

    from a deck of 52 cards,,, 13 are chosen at random. Calculate the joint probability mass function of the #'s of hearts, clubs, diamonds and spades that are selected.
    Last edited by Andreamet; March 26th 2008 at 03:26 PM.
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    I think this is a bivariate statistic

    Quote Originally Posted by Andreamet View Post
    from a deck of 52 cards,,, 13 are chosen at random. Calculate the joint probability mass function of the #'s of hearts, clubs, diamonds and spades that are selected.
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    Quote Originally Posted by Andreamet View Post
    from a deck of 52 cards,,, 13 are chosen at random. Calculate the joint probability mass function of the #'s of hearts, clubs, diamonds and spades that are selected.
    Read this thread - this time you have a multinomial distribution with n = 13 and pr(heart) = pr(spade) = pr(diamond) = pr(club) = 1/4.
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    Quote Originally Posted by Andreamet View Post
    from a deck of 52 cards,,, 13 are chosen at random. Calculate the joint probability mass function of the #'s of hearts, clubs, diamonds and spades that are selected.
    If the choosing is done without replacement, the pmf will be a multivariate hypergeometric distribution:

    p(h, d, c, s) = \frac{ {13 \choose h} {13 \choose d} {13 \choose c} {13 \choose s}}{ {52 \choose 13} }

    where h + d + c + s = 13.

    You could also build in the h + d + c + s = 13 restriction and write it as:

    p(h, d, c, s) = \frac{ {13 \choose h} {13 \choose d} {13 \choose c} {13 \choose {13 - h - d - c}}}{ {52 \choose 13} }.
    Last edited by mr fantastic; March 31st 2008 at 05:56 AM.
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