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Unformatted text preview: of & is equal to the length of the subinterval. For n 1, define the following random sequences: a. n n = ) ( U b. -= 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. 6. 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? 7. 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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- Spring '08