Let w = Ax - By where A and Bare rx q an rx p matrices of known constants and y and x are random vectors. a) find μw and Σw. b) if (y, x)' is jointly multivariate normal, use the mgf technique to find the distribution of w

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A: It is an important part of statistics . It is widely used .

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A: * SOLUTION :-  Based on the above information we prove that X and Y are independent random…

Q: Derive the Least Squares Estimator 3 of the parameter 3 in the no-intercept model Y₁ = Bα₁ + Ei,

A: Hi! Thank you for the question. As per the honor code, we are allowed to answer 1 question at a…

Q: a) Find P(X1 > X2 + X3 + 2). b) Find P(X1 > 2|X2 = 1, X3 = 1).

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Q: A point is randomly selected with uniform probability in the X-Y. Plane within the rectangle with…

A: Introduction :

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A: We are given here that:P(X = 1) = P(X = 2) = P(X = 3) = 1/3 as X is a discrete uniform distribution…

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A: Given: X and Y be two random variables and let r, s, t, and u be real numbers.  We have to show that…

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A:

Q: Let X1 and X2 be two independent normal random variables with parameters (0,1) and (0,4)…

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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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A: Given: There are three vectors.

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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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A: We know, any linear combination of normal distribution is a normal distribution. Here, x1 and x2 are…

Q: Show that (a) Cov(aX, bY)= ab Cov(X,Y). (b) Cov(X+a, Y + b) = Cov(X,Y). (c) Cov(X, aX+b) = a Var(X).

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A: A random variable X is called to follow the Bernoulli distribution if it takes only non-negative…

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Q: Let X, Y and Z be three independent random variables such that E(X)-E(Y)=E(Z)=1 and…

A: Solution: Given, E(X)=E(Y)=E(Z)=1 E(X^2)=E(Y^2)=E(Z^2)=10

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A: Given information: It is given that X be a sample from a bivariate normal population.

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Q: Suppose Y, and Y, are random variables with joint pdf (6(1– y2), 0 < y1 < y2 0, otherwise Let U1 and…

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Q: Let Z₁ and Z₂ be independent standard normal random variables. Let pe [-1, 1]. Find a matrix L such…

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Q: 4- Independent bivariate Gaussian samples {x(0), x(1),...,x(N − 1)} are observed. Each observation…

A: Solution: From the given information, Here,