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**1. Homework Statement**

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. Homework Equations**

Marginal pmf for X is P

_{x}(x) = P(X=x) = [tex]\sum[/tex] P(x,y)

Conditional pmf for Y given X=x is P

_{Y/X}(y,x) = P(x,y)/P

_{x}(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 P

_{x}(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

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