Suppose that X E U(0,1). Let X(1),X(2), X(3) be the order variables corresponding to a sample of 3 independent observati

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Suppose That X E U 0 1 Let X 1 X 2 X 3 Be The Order Variables Corresponding To A Sample Of 3 Independent Observati 1 (49.3 KiB) Viewed 97 times

Suppose that X E U(0,1). Let X(1),X(2), X(3) be the order variables corresponding to a sample of 3 independent observations of X. Define random variable Yı,Y,Yz as follows: X(1) Y = X(2) X(2) X(3) X2 Y2 Yz = X(3) = (a) [6 points] Find the joint density function of Yı, Y, and Y3 (b) [6 points] Show that Yı, Yz, and Y3 are independent. (c) [8 points] Show that Yı, Yz, and Y3 are all uniformly distributed. (Here Y? means the square of Y, and Yž means the cube of Y3)