Question: 10.3.2 Let X I , . . . , X , be a random sample selected from the U[O, 11 distribution. (i) Show that the

10.3.2 Let X I , . . . , X , be a random sample selected from the U[O, 11 distribution.

(i) Show that the distribution of X j , , is BETA(j, n - j + 1) for j = 1, . . . , n. (ii)

Find the distribution of a sample median Xk+l:,, and obtain its variance if n =

3,7,15,2k + 1. Do you see any trend?

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