A little confused on a past exam problem, thank you for your help!

(6+9=15 points) (a) Let X1, X2, ..., X20 be a random sample from Uniform(a-B, a+ B) distribution with pdf f(x) = 28 if a - BSISa+B otherwise Obtain the Method of Moment estimator a, 8. Obtain the estimates if )_ Xi = 30, El(X, - X)? = 100. Show steps. Recall that (a + b)3 = a3 + 3a-b + 3ab- + 63. (b) Suppose X1, . .., Xs are i.i.d. from N(0, 1) and Y1, ..., Ys are i.i.d. from Exponential(1) distribution, and they are all independent. What are the distributions of (i) X3/}(X; + X; + X]), X3+X2 (ii ) 2x- +X;+x7: (iii) X7 + X3 + X3 + X7, (iv) Y6 + Y7 +Ys, (v) YetViews: (vi) 2Yi + X]. No derivation or explanation is needed. Only mention the name of the dis- tributions along with parameters (if any). Each has 1.5 points. No partial credits