Let us consider the experiment of rolling a die twice and define Ω = {(1, 1),...

Question

Question

Let us consider the experiment of rolling a die twice and define Ω = {(1, 1), · · · ,(6, 6)}

which contains all 36 possible outcomes. Assume that all outcomes are equally likely:

P({ω}) = P({(i, j)}) = 1/36 for all i, j = 1, 2, · · · 6.

Thus, (1, 2) ∈ Ω corresponds to the first outcome being 1 and the second outcome being 2. Define

X = i, if the first outcome is i, i = 1, 2, 3, 4, 5, 6.

and Y = sum of the two outcomes.

Solve the following problems.

1. Express X and Y as functions of ω, as done in class.

2. Find the pmfs of X and Y

3. Find the joint pmf of X and Y Are X and Y independent?

4. Find the expected values of X and Y .

MUST SHOW ALL WORK FOR FULL CREDIT!!!

Answer 1

Answer #1

Answer 2

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