Question: Please provide typed solution with explanation and justification for each part asap Prove, or provide a counterexample to disprove the following for all discrete proba-
Please provide typed solution with explanation and justification for each part asap

Prove, or provide a counterexample to disprove the following for all discrete proba- bility distributions P, all events A and B, and all random variables X and Y: (a) P(A \\ B) 2 P(A) - P(B) (6 marks) (b) If 0 E(X)) 24 (4 marks) (d) If E(X) > E(Y) then P(X > Y) > 0 (4 marks)
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