Here are four different joint PMFs:

(a) For each pair of random variables, indicate whether the two random variables are independent, and compute the correlation coefficient p.

(b) Compute the least mean square linear estimator U_L(V) of U given V. What is the mean square error? Do the same for the pairs X, Y, Q, R, and S, T.

y=-1 | 1/9 y=011/9 y=111/9 1/9 1/9 1/9 1/9 1/9 1/9 u -1 | 0 0 1/ u=0 0 1/3 0 v-11/3 00 t=-111/6 0 1/3 0 1/6 0 1/6 0 t=111/6 r=011/12 r=1 | 1/6 1/6 1/12 1/121/12 UL(V) of U