Suppose S 1234 and P1 12 P2 2P3 4P4 Compute P 1 P 2 P 3

Suppose S = {1,2,3,4}, and P({1}) 1/2 = P({2}) = 2P({3}) = 4P({4}). Compute P ({1}), P ({2}), P ({3}), and P ({4}).

Note that it has to be that the probabilities sum up to 1,

P{1} + P{2} + P{3} + P{4} = 1

In terms of P{2},

[P{2} + 1/2] + P{2} + P{2}/2 + P{2}/4 = 1

11 P{2}/4 + 1/2 = 1

11 P{2}/4 = 1/2

P{2} = 2/11

Thus,

P{1} = 15/22

P{2} = 2/11

P{3} = 1/11

P{4} = 1/22 [ANSWERS]