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