Suppose the random variables X,,X2,X; have the population variance/covariance matrix: 1 -2 0 E=-2 0 1 Calculate the principal components and interpret their meaning. What can be gained from knowing these values?

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Q: (b) Let X - 3 (u, E) with the date matrix [5 3 4 || x1 X =|2 1 3 X2 Find the variance- 5 6 4x3…

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A: Solution

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Q: If a square matrix M has a stable distribution, then it must be regular

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Q: a) Let X = X,, X,, X, be a random vector and %3! let the data matrix for X be 2 5 3 4 2 4 2 3 Obtain…

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Q: Let X ∼ U(a, b). Use the definition of the variance of a continuous random variable (Equation 2.38…

A: The mean of X is given by:

Q: 3. Consider the MA(2) model y, = E, + Bɛ,-2. where < 1 and (ɛ,) WN(0, 1). (a) Find the…

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A: If X and Y are independent. Then , Given that E(X) = 45, V(X) = 60 E(Y)= 67 , V(Y)= 125 W = 2X+4Y…

Q: matrix for a portfolio with 50 stocks requires the calculations of ____ variances an

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Q: (b) The variance-covariance matrix of three random variables X,, X, and X, is given by : 1 0.36 0.49…

A: the variance covariance matrix of three random variable    ∑ = 10.360.490.3610.250.490.251

Q: sample covariance matrix S as s- () 4 S = 6

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Q: If X and Y are two independent random variables, then E(XY) = E(X) E(Y)

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Q: Use this covariance matrix to find the estimated variance of the estimated mean of y when z = 8.…

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Q: [1 The matrix 3 is a 4 3 variance-covariance matrix of two random variables.

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

Q: X and Y are independent. If we are given P(X = 0) = P(X =1) = P(X =2) = }, P(Y = 1) = 3. P(Y = 2) =…

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Q: Let X, and X, be independent random variables. Suppose the mean of X, and X2 are 2.5 and 3; and…

A: We have to solve given problem:

Q: If X and Y are any random variables with COV(X, Y) = 0.25, o = 0.36, and o = 0.49, then the…

A: From the given information, Covx,y=0.25         σ2x=0.36         σ2y=0.49 Thus,

Q: prove the below Theorems (mean and variance of each) If Y is an exponential random variable with…

A: Given that

Q: For the random variable transformation Y=X*X, the value of the expectation of Y is equal to E[Y]

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Q: what is E[XY]?

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Q: Let x be a D-dimensional random variable with Gaussian distribution N(x | 4,E), be A a non-singular…

A: the problem can be solved using the concept of expectation.

Q: Let X and Y be two random variables with E (X) = 1, E (Y) = 2, Var (X) = 1, Var (Y) = 2, !! Cov (X,…

A: Given that the mean of aX+bY is 3  So,  E(aX+bY)=3aE(X)+bE(Y)=3a(1)+b(2)=3a+2b=3a=3-2b ..........(Eq…

Q: X A В X 3.56 -1.00 -2.89 -1.44 A -1.00 В -2.89 C -1.44 -0.07 0.47 3.16 3.38 2.13 -0.07 2.13 3.51…

A: We have given that covariance matrix in which four variables X, A, B and C.

Q: Let X and Y be two independent exponential random variables. X ~

A: Given,  X and Y be two independent exponential random variables.                       X~exp(1) and…

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Q: The position and elevation of a survey station are given by the random vector x= x, in |X3 which X,…

A: Hi, there! since, the multiple questions are posted, we are allowing solving first question. Kindly…

Q: Let X,, X2 and X, be independent and identically distributed N4(0,E) random vectors, where E is a…

A: *Answer:

Q: Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete…

A: For the given data Find the covariance and correlation between x and y

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: Find the variance of X + 3Y + Z + 6 in terms of the variances and covariances of X, Y, and Z.

A: Given:  X + 3Y + Z + 6

Q: Suppose Y₁,..., Yn are i.i.d. random variables with Y; ~ N(u, o). Express the following vector in…

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Q: A random variable X has a probability distribution as X a b C P(X) = |p(x) 1/4 1/2 1/4] It is…

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Q: Suppose that you have the following model and data to estimate the following equation  Nobs Y X2…

A: The given data is Y X2 X3 1 1 3 2 2 2 4 4 5 3 3 4 2 5 1 We have to a. Find the OLS…

Q: Suppose the random variables X1, X2,X, have the population variance/covariance matrix: -2 0 E=-2 5 0…

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Q: Suppose Z,,Z,,Z¸ are standardized variables with 6. ( 1 0.8 0 covariance matrix p= 0.8 0 1 (a) (b)…

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Q: 6. Let the random variables X and Y have the joint p.m.f. F(x,y) = 32 x+y x = 1, 2, y = 1,2,3,4.…

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Q: Example 10 : If X is a continuous random variable and Y = aX + b, prove that = a E(X) + b and V(Y) =…

A: It is given that Y=aX+b.

Q: 1. Imagine 3000 students took an exam, where the max score is 200. The average was 80 and the…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.