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First thing comes to my mind is to use order statistics to do part 2. (because 5 numbers are given). And the first estimator comes to my mind is 6/5 * X(5) --- where X(5) is the maximum number of the 5. In general, (n+1)/n * X(n) is an unbiased and consistent estimator of c. (correct me if...

I could only solve in a regular way, which is: E[X] = 1 + E[Y|X1 = a] E[Y|X1 = a] = 1/4 * (1+ E[Y|X1 = a]) + 3/4 * (1 + E[Z|X1 = a, X2 = b]) E[Z|X1 = a, X2 = b] = 1/2 * (1 + E[Z|X1 = a, X2 = b]) + 1/2 * (1 + E[W|X1 = a, X2 = b, X3 = c]) E[W|X1 = a, X2 = b, X3 = c] = 3/4 * (1 + E[W|X1 =...