Consider the underlying probability space ($1.7. P). where (2 = [1,1], .7: = 36?[1,1], the Borel Ualgebra 011 [1, 1]. and P([a. bl) = ab a). for any interval [(111)]. Consider a random variable X : 52 > [0.1] given by X(w) = |w|. Let 1:" = {X_1(B) : B E 9610, 1]}. 0 Show that J} 75 .7: by nding an event. A in .7: but. not in .7}. (Note: f is called the aalgebra generated by X ). 0 Let Y be another random variable: Y(w) = %(w -| 1). Is Y measurable with respect to ($2, f), ([0, 11.3510, 1])? Justify your