Answered: Example 3.1 (x1x2x3 Let X = (X₁, X2,… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 13EQ

See similar textbooks

Related questions

Question

Please Provide correct answer ASAP

Example 3.1
(x1x2x3
Let X = (X₁, X₂, X3) be a discrete type random vector with p.m.f.
if (x₁, x2, x3) = {1, 2} × {1, 2} × {1,3}
otherwise
72
(0,
(i) Find the conditional p.m.f. of X₁ given that (X₂, X3) = (2,1);
(ii) Find the conditional p.m.f. of (X₁, X3) given that X₂ = 3.
fx (x1, x2, x3):
=
)

Expert Solution

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Let X = (X₁, . . . , Xn) denote an (n × 1) vector of independent random variables Xi∼ N (0, 1), i = 1, . . . , n. Let A = [aij] denote an (m × n) matrix, and define a random vector Y = (Y₁, . .. , Ym) asY = AX. Show that Cov(Yi, Yj) Which of the following lines is a valid argument? See attached pic
Human blood types are classified by three gene forms A, B, and O. Blood types AA, BB, and OO are homozygous, and blood types AB, AO, and BO are heterozygous. If p, q, and r represent the proportions of the three gene forms to the popula-tion, respectively, then the Hardy-Weinberg Law asserts that the proportion Q of heterozygous persons in any specific population is modeled by Q(p, q, r) = 2(pq + pr + qr), subject to p + q + r = 1. Find the maximum value of Q.
Which of the following can be a Probability Vector. a) [-0.1 0.8 0.1] b) [0.1 0.6 0.2 ] c) [0.1 0.3 0.6]
Let P be a 2 × 2 stochastic matrix. Prove that there exists a 2 × 1 state matrix X with nonnegative entries such that PX = X.
Consider the information below relating to the monthly rates of return for two companies X and Y over a period of 4 months: Y 2 xRate of return yRate of Return Date Month 1 -4.76 -4.75 Month 2 5.34 7.65 Month 3 12.09 6.98 Month 4 -2.98 9.65 Calculate the covariance per month between the two companies. Show all your working.
CONDITIONAL AND MARGINAL PROBABILITY - Statistics and probability } 1) In a plant, complex components are assembled on two different assembly lines, A and B. Line A uses older equipment than B, so it is a bit slower and less reliable. Suppose that on a given day line A assembles 8 components, of which 2 have been identified as defective (D) and 6 as non-defective (ND), while B has produced 1 defective and 9 non-defective components. . a) What is the probability that, when selecting a component at random, a defective one will come out? b) If the selected component is defective, what is the probability that it has left line A? What is the probability that it came out of line B?
A population with three age classes has a Leslie matrix L. If the initial population vector x0, compute x1, x2, and x3
. A population with two age classes has a Leslie matrix L . If the initial population vector x0, compute x1, x2, and x3
Q3. Use the following data set of 6 observations relating to 7 variables to construct a similarity matrix by: Matching Coefficient method. Jaccard’s Coefficient method. Observation A B C D E F G 1 1 1 0 0 1 0 0 2 1 1 1 1 0 0 1 3 1 0 1 0 0 0 0 4 0 1 0 0 1 1 0 5 0 0 0 1 1 1 1 6 0 0 0 1 0 1 0
Let W be an m X 1 vector with covariance matrix ƩW, where ƩW is finiteand positive definite. Let c be a nonrandom m X 1 vector and let Q = c'W.a. Show that var(Q) = c'ƩWc.b. Suppose that c ≠0m. Show that 0 < var(Q) 6 ∞
Let X = (X1, X2, ..., Xn)T be a random vector with mean vector μ and covariance matrix Σ. Suppose that for every a = (a1, a2, ..., an)T ∈ Rn, the random variable aTX has a (one-dimensional) Gaussian distribution on R. a) For fixed a ∈ Rn, compute the moment generating function MaTX(u) of the random variable aTX, writing the answer using μ & Σ. b) Define MX(t1, t2, ... , tn), the moment generating function of the random vector X, and express it in terms of MtTX, the moment generating function of tTX where t = (t1, t2, ..., tn). c) Combining a) and b), compute the moment generating function MX(t) of X and hence prove that the random vector X has a Gaussian distribution.
Let X be an n-dimensional random vector and the random vector Y be defined as Y = AX + b, where A is a fixed m by n matrix and b is a fixed m-dimensional vector. Show that CY = ACXAT .

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS