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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- Mar 24th 2008, 06:28 PMAndreametjoint 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.

- Mar 26th 2008, 03:26 PMAndreamet
- Mar 27th 2008, 03:07 AMmr fantastic
Read this thread - this time you have a multinomial distribution with n = 13 and pr(heart) = pr(spade) = pr(diamond) = pr(club) = 1/4.

- Mar 31st 2008, 05:42 AMmr fantastic
If the choosing is done

**without**replacement, the pmf will be a multivariate hypergeometric distribution:

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

where h + d + c + s = 13.

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

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