Let Anand B, be the random variables. A X (1) An cos ont+ Bp sin ont, where aon is a real constant. Find the power density spectrum of X (1), if A, and B, are uncorrelated random variables with zero mean and same variance.

Q: Determine the variance of Z.

A: Helpful formulas (i)VaX=a2VX(ii)VC=0,where c is the constant(iii)VaX+ bY=a2VX+ b2VY

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Q: Consider that X₁, X₁...... X are random variables and the variance of each variable is 1 and the…

A: Given that V(X1)=V(X2)=...+V(Xn)=1 and r(Xi,Xj)=14i≠jWe have to calculate V[X1+X2+...+Xn]

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

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Q: Let X1,..., X, be iid with mean u and finite variance o?. Consider the following estimator for u: 1…

A: a.) Here, T=1n-1∑i=1nXiThen E(T)=1n-1E∑i=1nXi=∑i=1nE(Xi)n-1=nμn-1Hence, the bias of T is…

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Q: Let X be a standard normal RV. Suppose Y = 2X+3 and Z = -X+6. a) Find the covariance between Y and…

A: Here we have given X is standard normal variate Y = 2X+3 AND Z =-X+6 We have to find the following.

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A: Given information: X~Uni(a=1,b=4) Standard deviation of X is: σX=b-a12       =4-112       =0.8660…

Q: Let X and Y be random variables. Suppose Var(X) = 1.6, Var(Y) = 1.2, an

A: Given information: Var(X)=1.6 Var(Y)=1.2 Cov(X,Y)=0.6 Let  Z = -1.2X + 1.9Y + 4.2.

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Q: Let Xi and Yi be random variables with Var(Xi) = σx2 and Var(Yi) = σy2 for all i ∈ {1, . . . , n}.…

A: It is given that: varxi=σx2varyi=σy2 and xi and yi are independent and corrxi,yi=ρ

Q: 3. Let X and Y be continuous random variables with joint PDF S3x 0<y<x<1 f(x,y) = otherwise…

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Q: Suppose that a random voltage V supplies a random current I through a constant resistive load. What…

A: The correlation between the random variables V and I is given by ρV, I=CovV, IVarV·VarI.

Q: 1. Let fx(x) denote the PDF of X, evaluate fy(y), the PDF of Y = --X – 6, in terms of fx(x).

A: Given problem is :

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Q: obtain the MVB estimator for u in normal population. №.(402), where 2 is know

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Q: If X₁, X2, ..., Xn constitute a random sample of size n from an exponential population, show that X…

A: let X1, X2, ......Xn is an independent identically distributed random variable following an…

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A: (a) The covariance between Xi and Yi is given by: Cov(Xi, Yi) = E[(Xi - E[Xi])(Yi - E[Yi])] Since…

Q: We have the following information about the independent random variables X and Y: of = 5.4 and o=…

A: σx2=5.4,σy2=7.7

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A: Given: X1,X2, ....... ,Xn ~Nμ, σ2Sample mean = X¯nSample variance = Sn2

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Q: Let X and Y be random variables. Suppose Var(X) = 1.6, Var(Y) = 1.5, and Cov(X, Y) = 0.1. Let Z =…

A: Solution: From the given information, Var(X) =1.6, Var(Y) =1.5 and Cov (X, Y) =0.1. Let Z =…

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Q: Let fx(x) denote the PDF of X, evaluate fy (y), the PDF of Y = -X – b, in terms of fx(x). %3D a

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: 6) Consider the random variable Z₁ = cos (2 * π * Yn/n) where Yn is binomial(n,p) a. What is its…

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Q: 3. Let X and Y be i.i.d. standard normal random variables. Find E[X2 +Y²] and EVX² +Y².

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Q: 4. Suppose the joint PDF of two random variables X and Y are given below. |3(ry? + x²y), if 0 < x <…

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Q: Q2: (b) Let X₁, X2, X3 be uncorrelated random variables, having the same variance o². Consider the…

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Q: 0². Find expressions for the following in terms of the mean and variance:

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Q: . Find the joint density function of the random variables Z = X + Y and W = 2X −Y . What is the…

A: Let X and Y be independent Gaussian random variables, each distributed according to (0, σ2). Let , Z…

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Q: Suppose X and Y are two independent variables with variance 1. Let Z = X+bY where b > 0. If Cor(Z, Y…

A: Given that, V(X)= V(Y)= 1 So  V(Z) = V(X+bY)  = V(X)+b2V(Y)  { x and Y are independent} = 1+ b2

Q: Let Xi- N co,1) and n=2 auel T= Xi+ Xz Show that Tis a %3D Sufficiency Stabisuic Statistic.

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