The density function of Xis (2(x-1), f(x)= (a) Find the mean E(4X+3); (b) Find the variance σ3x+2. 0, 1 < x < 2, elsewhere.

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A: Given  yt=c+βt+εt  , where εt~WN0, σ2

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A:

Q: 3. x and y are independent zero mean Gaussian random variables with variance of and o3. Let z = (x +…

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A: a) If X and Y are uncorrelated then Cov(X,Y)=0, given V(X)=V(Y)=25 Answer(a): 50

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A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

Q: Let X and Y be random variables with Var(X)=0.64, Var(Y)=0.81, and Cov(X,Y) = 0.5. Find each of the…

A: Step 1: a) It is given that, Var(X) = 0.64, Var(Y) = 0.81 and Cov(X,Y) = 0.5. The coefficient of…

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A: It is given that   Var(X) = 1 Var(Y) = 2

Q: None

A: Step 1: Step 2: Step 3: Step 4:

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A: X~exp(ɑ)

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A: From the provided information,

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A: Let's break down the given probability mass function (pmf) for the discrete random variable…