Question: Let X = (X 1 , ...,X k ) be a random vector with a covariance matrix C, and t = (t 1 , ...,

Let X = (X₁, ...,X_k) be a random vector with a covariance matrix C, and t = (t₁, ..., t_k) and ˜t= (˜t₁, ..., ˜t_k) be two non-random vectors. Consider two linear combinations: ⟨X, t⟩ and ⟨X,˜t⟩. Generalizing (2.1.4), prove that Cov{⟨X, t⟩, ⟨X,˜t⟩} = ⟨Ct,˜t⟩. Can we switch t and˜t in the r.-h.s. of this formula? Why? Let X = (X1, ...,Xk) be a random vector with a covariance

Step by Step Solution

★★★★★

3.39 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Without loss of generality we can ass... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Probability And Stochastic Modeling Questions!

Let X be a random vector that is split into three parts, X = (Y, Z, W). Suppose that X has a continuous joint distribution with p.d.f. f (y, z, w). Let g1(y, z|w) be the conditional p.d.f. of (Y, Z)...

8. What is the proper preparation sequencing of the following budgets? 1. Budgeted Balance Sheet 2. Sales Budget 3. Selling and Administrative Budget 4. Budgeted Income Statement a. 1, 2, 3, 4 b. 2,...

The vector spaces N(A), R(A), N(AT), R(AT) are the four fundamental subspaces associated with a matrix A. We can use MATLAB to construct orthonormal bases for each of the fundamental subspaces...

Let X be a two- element zero- mean random vector. Suppose we construct a new random vector Y according to a linear transformation, Y = TX. Find the transformation matrix, T, such that Y has a...

Part I: (20pts) Consider a portfolio that invests 100 w% of its fund into Amazon, 100 w2% into American Airlines, and the rest into Boeing. Let X = (X1, X2, X3)' = R be a random vector representing...

Let X = [X X2 eigenvector/eigenvalue Xp] be a random vector with covariance matrix . The pairs of are given by (e, A;) for i = 1,..., p. The ith principal component is given by Y; = eX. The...

8.4.12 Let X be a random vector with cor- relation matrix Rx and covariance matrix Cx. Show that Rx and Cx are both pos- itive semidefinite by showing that for any nonzero vector a, a Rxa 20. a'Cxa 0.

Let X = (X 1 , X 2 ) be a two-dimensional normal random vector; E{X 1 } = 1, E{X 2 1 } = 5, E{X 2 } = 2, E{X 2 1 } = 13, E{X 1 X 2 } = 2. (a) Write the density of the centered vector Y = Xm, where...

1). On a busy Sydney y crossroad , traffic accidents happen almost every week . The distribution of the number of accidents in a week is believed to be Poisson. Then the numbers of accidents observed...

3.5 Let X : p 1 denote a vector of random variables representing various observable quantities related to learning rate, and suppose for > 0, L(X|, ) = N(, ). It is found that the first q variables...

You are the lead manager of a large mutual fund. You have become aware that several equity analysts who have recently joined your management team are interested in understanding the differences...

Joe, who is married (Julia, age 34) and the father of one (age 4), is 38 years old and expects to continue to work until age 67. He earns $90,000 per year and expects annual salary increases of 2%....

12. The heights of three plants A, B and C in a garden are in the ratio 2:3: 5. Their mean height is 30 cm. (i) Find the height of Plant B. (ii) If another Plant D is added to the garden such that...

Opportunity obsession. Such entrepreneurs are aware of market and customer needs. LO.1

Ask the class members to think of places they have worked or organizations they have been associated with. They should identify decisions that they observed being made by people within the...

Which ethical viewpoint do you think is the best? Describe the viewpoint and explain your choice.

Using the three-component model for creativity, which area do you believe would be easiest for managers to affect? Why?

As a result of a slowdown in operations, Tradewind Stores is offering employees who have been terminated a severance package of $107,000 cash paid today; $107,000 to be paid in one year; and an...

#include #include const int MPU _ addr = 0 x 6 8 ; / / I 2 C address of the MPU - 6 0 5 0 int 1 6 _ t AcX,AcY,AcZ,Tmp , GyX , GyY , GyZ; float delta _ t = 0 . 0 0 5 ; float pitchAcc,rollAcc, pitch,...

The relationship between the value of an annuity and the level of interest rates is as follows: The present value of an annuity rises as r drops; the future value of an annuity falls as r drops....