(solution) Let (O,.F i ,Pi) be Lebesgue measure on [0,1]. Consider a second probability triple, (O 2 ,-F 2 ,P…

(solution) Let (O,.F i ,Pi) be Lebesgue measure on [0,1]. Consider a second probability triple, (O 2 ,-F 2 ,P…

Let (Ω,.Fi,Pi) be Lebesgue measure on [0,1]. Consider a second probability triple, (Ω2,-F2,P2)  defined as follows: Ω2 = {1/2}, Ti consists of all subsets of Ω2, and P2 is defined by P2J1} = 3, P2{2} = | , and additivity. Let (Ω,F,P) be the product measure of (Ω1 ).F1 ,P1 )and(Ω2 ,.F2 )P2 ). (a) Express each of Ω, F, and P as explicitly as possible. (b) Find a set A e T such that P(A)=3/4