Petya and Vasya are playing the following game. Petya chooses a non-negative random value ξ with expectation E[ξ]=1, after which Vasya chooses his own value η with expectation E[η]=1 without reference to the value of ξ. For which maximal value p can Petya choose a value ξ in such a way that for any choice of Vasya's η, the inequality P[η≥ξ]≤p holds? inequalitiesprobability and statsexpectationcalculusintegrationprobabilityfunction