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Probability question using r.v. X and Y what is W=min(X,Y) ?

  1. Mar 31, 2009 #1
    1. The problem statement, all variables and given/known data
    Y
    -----------1----2-----3------4
    x---1----1/4----0-----0------0
    ----2----1/8----1/8---0------0
    ----3----1/12---1/12--1/12---0
    ----4----1/16---1/16--1/16--1/16

    The Joint PMF of random varables X and Y is given in the table above
    Let W=min(X,Y) and Z = max(X,Y)

    Find the marginal PMF Pw(w) of w ?
    (I don't understand what is meant by W=min(X,Y)

    Find the marginal PMF Pz(Z) of Z?
    Z = man(Z,Y)

    2. Relevant equations

    Pw(w) = SUM Pxy(x,y) ; where the sum starts at (x,y):g(x,y) = w

    3. The attempt at a solution

    Pw(1) = 0
    Pw(2) = 0
    Pw(3) = 0
    Pw(4) = 0

    or

    Pw(1) = 1/4 as 1 is the min of x and y

    Pz(1) = 1/16
    Pz(2) = 1/16
    Pz(3) = 1/16
    Pz(4) = 1/16

    Thanks in advance
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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