Question: Suppose X 1 ,X 2 ,X 3 are i.i.d. random variables, each uniformly distributed on {1, 2, 3}. Find the probability function for X 1

Suppose X₁,X₂,X₃ are i.i.d. random variables, each uniformly distributed on {1, 2, 3}. Find the probability function for X₁ + X₂ + X₃. That is, find P(X₁ + X₂ + X₃ = k), for k = 3, . . . , 9.

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