Let {2,}-WN (0,0) and let c be a constant, consider the process x, = z, cos(ct) + z₂ sin(ct). Find the mean and autocovariance function and determine whether the process is stationary or not. Consider the process x, u, sin(27)+u, cos(2721), where u, and u, are independent, zero mean random variables with variance. Show whether {x} is a stationary process or not.

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Q: 2. Define the process, t I VY(u)dW(u) + | Vudu Y(t) = What is the variance of Y (t)?

A: Solution Given   Y(t)=∫0tY(u)dW (u)+∫0tuduwe need to find the Y(t)?

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A: The provided information is as follows:. and  are independent random variables..

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Q: (a) Let X be a random variable with PDF ƒ(x) = 1−|x|, |x| ≤ 1. Obtain the MGF of X. (b) Find the PDF…

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Q: The joint pmf for X and Y is given in the accompanying table. (1) Find the marginal pmf's for X and…

A: The joint pmf for X and Y is given in the accompanying table

Q: 5 Find the mean and variance of Y =x (1) - dt теаn %3D

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Q: F(x,y) = { (x+y)/42 ; x = 1,2,3  y = 1,2                 0; elsewhere ] (i) Find the mean for the…

A: F(x,y) : { (x+y)/42 ; x=1,2,3 y=1,2  ; 0 elsewhere } Mean : E(X) = sum(x*P(x))

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Q: Suppose that Var(X) = 3, Var(Y ) = 4, and Cov(X,Y ) = 1. (a) Find Cov(2X −Y,X + 3Y ). (b) Find…

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A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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A: The given probability density of (X,Y) is given as, f(x,y)=6xy ; 0≤x≤1, 0≤y≤x0     ; O.W   Need to…