Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Distribution of card hands

  1. Nov 3, 2012 #1
    X = # of clubs in a 13 card hand drawn at random without replacement from 52 card deck
    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.
     
  2. jcsd
  3. Nov 4, 2012 #2

    chiro

    User Avatar
    Science Advisor

    Hey nikki92.

    The covariance of two random variables is given by Cov(X,Y) = E[XY] - E[X]E[Y] where E[XY] = Summation (over x) Summation over y P(X=x,Y=y)*xy (Or an integral for continuous random variable).

    The covariance matrix has Cov(Xi,Xj) at the (i,j) position in the matrix and note that Cov(Xi,Xi) = E[Xi^2] - {E[Xi]}^2 = Var[Xi] so you will have four entries with Var[X1], Var[X2] in (1,1) (2,2) and Cov(X,Y) in the other positions.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Distribution of card hands
  1. A card game (Replies: 3)

  2. Card probability (Replies: 10)

  3. Combination of cards (Replies: 16)

  4. Probability cards (Replies: 3)

Loading...