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Marginal/Conditional Probability Mass Functions

  1. Nov 15, 2008 #1
    1. The problem statement, all variables and given/known data
    A bag contains four dice labelled 1,...,4. The die labelled j has j white faces and (6-j) black faces, j = 1,...,4. A die is chosen at random from the bag and rolled. We define X = the number labelling the chosen die.
    Y = {0 if the face showing on the die is black; 1 if the face showing on the die is white.

    Construct a table displaying the values of the marginal pmf (probability mass function) for X and a separate table displaying the values of the conditional pmf for Y fiven X=x for general x.

    2. Relevant equations
    Marginal pmf for X is Px(x) = P(X=x) = [tex]\sum[/tex] P(x,y)
    Conditional pmf for Y given X=x is PY/X(y,x) = P(x,y)/Px(x)

    3. The attempt at a solution
    Okay so i know the two equations above for the two pmf's. I'm presuming that for the first part (marginal pmf) that you just use x=1,2,3,4 and that Px(x) is 1/4 for each value of x?
    For the second table I'm not so sure as I don't know which y values to put into my table, and how to work out any probabilities as it has to be for a general x and not a given value of x. As at the beginning of the question it states that y=0 or y=1 is it just these two values that i put into my table n then depending on when x=1,...,4 will alter the probability
    Last edited: Nov 15, 2008
  2. jcsd
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