Let be a sample space, and let a, b be two distinct outcomes. Consider the -algebra A = {, {a}, {a} ^c , } and a probability measure P : A [0, 1]. Let X be a real random variable on the probability space (, A, P) such that X(a) = 0.1 and X(b) = 0.2.

(A). Find X¹ ({0.2}).

(B). As we vary , what possible values can X() take?

(C). Suppose that P({a}) = 0.3. Completely specify the distribution of X (or characterize it in terms of a CDF, PDF, or PMF)