4. For the sake of consistency, let’s keep the same six-sided die with sides labeled 1, 2, 2, 3, 3, 3,but the questions we ask about it here will be unrelated to the previous problem.We roll this six-sided die three times. Let X be the number of times the die lands 1; let Ybe the number of times the die lands 2; let Z be the number of times the die lands 3.(a) Although there’s three variables, it’s enough to study the joint distribution of X and Y,because Z is a function of X and Y. What function? That is, what is Z in terms of Xand Y?(b) In the form of a 4 × 4 table, write down PXY(a, b), the joint PMF of X and Y.(c) In the form of a 4 × 4 table, write down PX|Y(a | b), the joint PMF of X given Y.(d) Explain what the X = 1, Y = 1 entry of your table in (c) means in terms of ourdie-rolling experiment and the faces that come up.
4. For the sake of consistency, let’s keep the same six-sided die with sides labeled 1, 2, 2, 3, 3, 3,
but the questions we ask about it here will be unrelated to the previous problem.
We roll this six-sided die three times. Let X be the number of times the die lands 1; let Y
be the number of times the die lands 2; let Z be the number of times the die lands 3.
(a) Although there’s three variables, it’s enough to study the joint distribution of X and Y,
because Z is a
and Y?
(b) In the form of a 4 × 4 table, write down PXY(a, b), the joint PMF of X and Y.
(c) In the form of a 4 × 4 table, write down PX|Y(a | b), the joint PMF of X given Y.
(d) Explain what the X = 1, Y = 1 entry of your table in (c) means in terms of our
die-rolling experiment and the faces that come up.
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