Let Y1 < Y2 < Y3 < Y4 < Y5 denote the order statistics of a random sampleof size 5 from a distribution having pdf f(x) = e−x, 0 < x < ∞, zero elsewhere.Show that Z1 = Y2 and Z2 = Y4 − Y2 are independent.Hint: First find the joint pdf of Y2 and Y4.

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A: Given that  Z1=Y1Y2Z2=Y2Y3Z3=Y3   Then,   Y3=Z3Y2=Z2Z3Y1=Z1Z2Z3

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.