Question: Please show all work! Please only do b and c! Let X1, X2, X3 be a random sample from a distribution. Hint: Derive the joint

Please show all work! Please only do b and c!

Let X1, X2, X3 be a random sample from a distribution. Hint: Derive the joint pdf of Y , Y2, Yz in parts (a) and (b). Also, note the following relation between the joint pdf of order statistics Xc.), X(2)...., Xem) and the joint pdf of the corresponding random sample X. X..... X, f(x(1), (2),.., X)=n! f(xy, X2,...,xn). a. X-Exponential (B). Prove or disprove that Y, XL) .Y X2) and Y, = X(3) are independent, where Xxx), i=1,2,3 denotes the ith order statistic. X(2) X(3) b. X-f(x)= . 00. X() X(2) X(3) the ith order statistic. c. Based on your conclusions for parts (a) and (b), would you claim that if the pdf of X is a member of X (2) *(1) scale parameter pdfs, then Y, XC) Y3 = .Y2 XN-1) Yn-1 and X(n) are independent? X(2) X(3) X(4) X(n) Explain

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