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 ﬁnite and the probability is one of ﬁnitely many upcrossings. (b) Repeat (a) with the change that you are asking about inﬁnitely 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
 Probability theory, Fµ, random process Xt

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