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 proba-bility 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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- Probability theory, Fµ, random process Xt