1 Question. Let S be the set of points contained in the circle of radius J? in R2, i.e. 1 s = {($1,222) | as? +m g } 1T Let 6' be the collection of all Lebesgue measurable subsets of 3 (please don't worry too much about this). Let P(A) be dened as the area of A, for every subset A of S which is measurable (i.e. a member of 5' - most subsets you can think of are measurable, so don't worry about this, it's just mentioned for completeness). Let (3,8,P) be the probability space we refer to, for this assignment problem. 1. Give examples of three non-empty independent events. 2. Give examples of three non-empty events that are pairwise indepen- dent but not independent. Please give explicit mathematical descriptions of all your events. For example, if your event is a square, you could deSCribe it by specifying its vertices, or the vertices on a diagonal, etc. If your event is a circle, you should specify the coordinates of the centre and the radius