Question: =+2.21. Let X1 < X2 < < Xn be order statistics for a random sample from the exponential distribution FX x expx for x

=+2.21. Let Xð1Þ < Xð2Þ < < XðnÞ be order statistics for a random sample from the exponential distribution FX ðxÞ ¼ expðxÞ for x 50.

ðaÞ Show that XðrÞ and XðsÞ  XðrÞ are independent for any s > r.

ðbÞ Find the distribution of Xðrþ1Þ  XðrÞ.

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