X = # of clubs in a 13 card hand drawn at random without replacement from 52 card deck(adsbygoogle = window.adsbygoogle || []).push({});

Y= # of queens in the same 13 card hand

the pdf of x is f_x (x) = (13 choose x)( 39 choose 13-x) / (52 choose 13) for x=< x =< 13

and o otherwise

the joint distribution of x and y = (13 choose x) ( 5 choose y) ( 34 choose 13-x-y)/ (52 choose 13) for 0 =<x =<13 0 =< y =< 4 0<=x+y<=13 and 0 otherwise

What is E(Y) and what is the covariance matrix (X,Y)?

E[Y] = Sum y=1 to 4 of y* (4 choose y)(48 choose 13-y)/ (52 choose 13) ?

I have no idea on the matrix.

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# Distribution of card hands

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