3. (Finite Stochastic Processes). We are given two urns as follows: Urn A contains 7 red marbles, 8 white marbles and 5 blue marbles. Urn B contains 4 red marbles and 3 white marbles. A fair die is tossed; if 1 or 4 appears, a marble is chosen from B, otherwise a marble is chosen from A. (i) Draw the tree diagram of the corresponding stochastic process. Find the probability that (ii) a red marble is chosen, (ii) a white marble is chosen, (iv) a blue marble is chosen.

4. [7.5 marks) Suppose X and Y are jointly continuous random variables with probability density function C[L+1], 0