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Unformatted text preview: X T ,T = R , are i.i.d. with X 1 L (1). (a) Choose a boundary function b t that is everywhere nite and the probability is one of nitely many upcrossings. (b) Repeat (a) with the change that you are asking about innitely many upcrossings. 4. Consider the random process X t = Y cos( t ) + Z sin( t ) for T = R ,Y N (0 , 1) ,Z E (2) . (a) Evaluate the expected value EX t . (b) If the covariance COV ( Y,Z ) = 0, evaluate the correlation function R X ( t,s ) = E ( X t X s ). (c) Under the above assumptions, evaluate EX 2 t and V AR ( X t ). 1...
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 '08
 WAGNER

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