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Unformatted text preview: = n n 1 1 ) ( V c. n n e ) ( W = d. n n 2 cos ) ( Y = e. ) 1 ( e ) ( Z= n n n Which of these sequences converges everywhere? almost everywhere? Identify the limiting random variable. 5. Let X n and Y n be two (possibly dependent) sequences of random variables that converge in the mean square sense to X and Y, respectively. Does the sequence X n + Y n converge in the mean square sense, and, if so, to what limit? 6. Show that if a n a and E[X n a n  2 ] 0, then X n a in the mean square sense as n ....
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 Fall '08
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