2) I need the resolution of this step-by-step exercise: The joint probability function of two discrete...
2) I need the resolution of this step-by-step exercise: The joint probability function of two discrete random variables X and Y is given by p (x, y) = (x + 2y) / 48, where x and y can assume integer values such that 0 ≤ x ≤ 2, 0 ≤ y ≤ 3, and p (x, y) = 0 in another case. Find P (X ≥ 1 | Y ≤ 2).
Homework Answers
P(Y < 2) = 1 - P(Y = 3)
= 1 - (P(0,3) + P(1,3) + P(2,3))
= 1 - (1/8 + 7/48 + 1/6)
= 1 - 7/16
= 9/16
P(X > 1 and Y < 2) = P(1,0) + P(1,1) + P(1,2) + P(2,0) + P(2,1) + P(2,2)
= 1/48 + 3/48 + 5/48 + 2/48 + 4/48 + 6/48
= 7/16
P(X > 1 | Y < 2) = P(X > 1 and Y < 2) / P(Y < 2) = (7/16) / (9/16) = 7/9
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