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Roll a fair four-sided die twice. Let X be the sum of the two rolls, and...

Roll a fair four-sided die twice. Let X be the sum of the two rolls, and let Y be the larger of the two rolls (or the common value if a tie).

a) Find E(X|Y = 4)

b) Find the distribution of the random variable E(X|Y )

c) Find E(E(X|Y )). What does this represent?

d) Find E(XY |Y = 4)

e) Find the distribution of the random variable E(XY |Y )

f) Explain why E(XY |Y ) = Y E(X|Y )

g) Find E(E(XY |Y )). What does this represent?

Math   Statistics-And-Probability   
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