Question: 1. Sample space of the random variable X X(S) S = {(1,1),(1,2),(1,3), (1,4),(1,5),(1,6) (2, 1), (2,2),(2,3),(2,4),(2,5), (2,6) (3,1),(3,2),(3,3),(3,4),(3,5),(3,6) (4, 1),(4,2),(4,3),(4,4),(4,5),(4,6) (5, 1), (5,2), (5,3),(5,4),(5,5),(5,6) (6,
1. Sample space of the random variable X X(S) S = {(1,1),(1,2),(1,3), (1,4),(1,5),(1,6) (2, 1), (2,2),(2,3),(2,4),(2,5), (2,6) (3,1),(3,2),(3,3),(3,4),(3,5),(3,6) (4, 1),(4,2),(4,3),(4,4),(4,5),(4,6) (5, 1), (5,2), (5,3),(5,4),(5,5),(5,6) (6, 1),(6,2),(6,3),(6,4),(6,5),(6,6)}\f2. X(i,j) = i - j for i,j e{1,2,3,4,5,6}, X(1,2) = 1 - 2 = -1, so X can take any value from -5,...,5 -5 sx$5 P(x = -5) = H(1,6)}1 151 36' P(x = -4) = H(1,5), (2,6)31 2 151 36' P(x = -3) = H(1,4), (2,5), (3,6)31 3 151 36' P(x = -2) = H(1,3), (2,4), (3,5) (4,6)31 4 151 36' P(x = -1) = H(1,2), (2,3), (3,4) (4,5) (5,6)31 5 151 36' P(x = 0) = H(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}1 6 151 = 36 P(x = 1) = H(2,1), (3,2), (4,3), (5,4), (6,5)31 5 151 36' P(x = 2) = H(3,1), (4,2), (5,3), (6,4)31 151 36' P(x = 3) = H(4,1), (5,2), (6,3)}1 151 363. F(x) = P(X SX), SO; Fx(x) = P(X
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