Given a fair coin and a fair 4 sided die, Jonathan and Joseph run the following experiment. They roll the die (let Y correspond to the random...

Given a fair coin and a fair 4 sided die, Jonathan and Joseph run the

following experiment. They roll the die (let Y correspond to the random variable associated with the roll).

If they roll a y they the flip the coin y number of times, let Z correspond to the random variable associated

with the total number of heads they flip.

1. Find the marginal PMFs of Y and Z (i.e. find P Y ( · ) and P Z ( · ) )

2. Find the conditional PMFs of Y and Z (i.e. find P Y | Z ( ·|· ) and P Z | Y ( ·|· )