Results 1 to 2 of 2

Math Help - URN

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    9

    URN

    An urn contains three white, six red and five black balls. Six balls are selected randomly. Let
    X and Y, respectively, be the numbers of white and black balls selected.
    a) Find p (X 1) X Y
    b) Find E[X | Y = 2]
    c) Are X and Y independent?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by sadasoria View Post
    An urn contains three white, six red and five black balls. Six balls are selected randomly. Let
    X and Y, respectively, be the numbers of white and black balls selected.
    a) Find p (X 1) X Y
    b) Find E[X | Y = 2]
    c) Are X and Y independent?
    a) Perhaps it's my fault but I don't understand your notation. If p (X 1) represents the probability that X is 1, then what is the X Y doing there?

    b) Y = 2, so the situation is the same as choosing 4 balls out of three white and six red. C(n, k) means n choose k.

    E[X|Y=2] = P(X=1|Y=2)*1 + P(X=2|Y=2)*2 + P(X=3|Y=2)*3

    = (1/C(9,4))*(C(3,1)*C(6,3)*1 + C(3,2)*C(6,2)*2 + C(3,3)*C(6,1)*3)

    c) No. As a simple counterexample, P(X=2) > 0, but P(X=2|Y=5) = 0.
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum