Please answer the following question

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(a) (5p) Suppose Z : R - R is non-decreasing. Show that Z is a random variable when both copies of R are equipped with their Borel o -algebras. (b) Let X, Y : 2 - R be continuous random variables on a probability space (2, F, P). (i) (5p) Suppose that -2 - and P(Y > 1) > Show that V ( Y ) > WIN (c) (5p) Urn A contains 4 red, 7 blue balls and 5 yellow balls. Urn B contains 5 red, 23 blue balls and 7 orange balls. We flip a fair coin. If the coin lands tails, then a ball is drawn from urn A. If the coin lands heads, then a ball is drawn from urn B. Suppose that a red ball is selected. What is the probability that the coin landed heads