6. Let X1, X2, X3 be a random sample from a distribution. 15 Points Hint: Derive the joint pdf of Y1, Y2, Y3 in parts (a) and (b). Also, note the following relation between the joint pdf of order statistics X (1), X (2),..., X (n) and the joint pdf of the corresponding random sample X1, X2,..., Xn f(x(1), (2), (n))=n! f(x1, x2,...,xn). a. X Exponential (B). Prove or disprove that Y₁ where X), i=1,2,3 denotes the ith order statistic. b. X f(x)= axa-1 0< x < 0, a >0. ' да X(1) = ,Y₂ X(2) = X (2) X(3) , and Y3 = X(3) are independent, Prove or disprove that Y₁ = X(2), Y₂ = X(3), , and Y3 = X(3) are independent, where X(), i=1,2,3 denotes 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 scale parameter pdfs, then Y₁ = , 1/₂ = X(1) X(2) X(2) x(3) X(3) ,Y3 = X(4) Yn-1 X(n-1), and X(n) are independent? X(n) Explain.