1.2.6 Let X and Y be independent random variables having distribution functions FX and FY , respectively....

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1.2.6 Let X and Y be independent random variables having distribution functions FX and FY , respectively.

(a) Define Z D maxfX;Yg to be the larger of the two. Show that FZ.z/ D FX.z/FY .z/ for all z.

(b) Define W D minfX;Yg to be the smaller of the two. Show that FW.w/ D 1????[1????FX.w/][1????FY .w/] for all w.

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An Introduction To Stochastic Modeling

ISBN: 9780233814162

4th Edition

Authors: Mark A. Pinsky, Samuel Karlin

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