Suppose the random variables X, Y, Z are obtained by spinning the adjoining roulette wheel, with X given by the outermost circle, Y given by the intermediate circle and Z given by the inner circle. (a) Calculate E[Z] (the expectation of Z). (b) Calculate E[X + YJ. (c) Calculate E[X • Z]. Is any of the three random variables X, Y, Z dependent on another? Justify your answer. (e) Are any of the three pairs (X, Y), (X, Z), (Y, Z) independent? If so, which? Justify your answer. (1) Compute P[Y=4 | Z=1]. (g) Compute E[Y|Z=1]. ( 2 .5 -3 1/6 1/12 | 1/12