Let X 1 , X 2 be the rolls of two four sided tetrahedron dice Let S X 1 X 2 be the sum of the dice Let M max(X 1 , X 2 ) be the largest of the two numbers rolled Find the following (a) E X 1 X 2 (b) E X 1 S (c) E M X 1 x (d) E X 1 X 2 X 1 ...

a By independence EX 1 X 2 EX 1 52 b Observe that S ESS EX ...

Let X 1 , X 2 be the rolls of two four-sided tetrahedron dice. Let S =

Question:

Let X₁, X₂ be the rolls of two four-sided tetrahedron dice. Let S = X₁ + X₂ be the sum of the dice. Let M = max(X₁, X₂) be the largest of the two numbers rolled. Find the following:
(a) E[X₁|X₂]
(b) E[X₁|S]
(c) E[M|X₁ = x]
(d) E[X₁X₂|X₁]