Question: Let (X, Y, Z)T, t2 0, be a joint-Gaussian process with each component a Brownian motion with means E[X] = -2t E[Y ] = t

Let (X, Y, Z)T, t2 0, be a joint-Gaussian process with each component a Brownian motion with means E[X] = -2t E[Y ] = t E[Z ] = -4t variances var(X) = t var(Y ) = 2t var(Z) = 9t and covariances cov(X, Y) = -min (t s) cov(X, z) = -2 min (t. s) cov(Y, z) = 4 min (t. s). Define the process G. = -t - 57 +2Y, t20. (a) Find the distribution of G, [3 marks]. (b) Determine if G, is a Brownian motion [3 marks]. (c) Using R, simulate a sample of G, of size n = 105 and assess the normality of the sample using an appropriate plot [3 marks]. (d) Using R, compute P(G, = 40|X, = -1) [3 marks]. Hint. Use R function pmvnorm from mvtnorm package. (e) Find var(G,|X, = -1) = cov(G2, G,|X, = -1) [3 marks]. (1) Find E [(( ) [X, = -1] [3 marks]

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

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 Mathematics Questions!

the correct IV or levels or DV in experimental hypotheses. A group of college students were given a short course in speed-reading. The instructor was curious if a monetary incentive would influence...

Let (X. Y. Z)T, t2 0, be a joint-Gaussian process with each component a Brownian motion with means E[X] = -2t E[Y ] = t E[Z ] = -4t variances . var(X) = t var(Y ) = 2t var(Z ) = 9t and covariances...

Let (X. Y. Z)T, t2 0, be a joint-Gaussian process with each component a Brownian motion with means E[X] = -2t E[Y] = t . E[Z] = -4t variances . var(X) = t var(Y) = 2t . var(z) = 9t and covariances...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

9/14/10 12:39 PM Page 381 Chapter dug84356_ch06a.qxd 6 Rational Expressions Advanced technical developments have made sports equipment faster, lighter, and more responsive to the human body. Behind...

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

The goal of this lab is to get a better understanding of X 8 6 ISA, assemble and disassemble code, and data movement with registers. ( I just need help with number 5 ) This lab needs a computer with...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

10 Green's functions for PDEs In this final chapter we will apply the idea of Green's functions to PDEs, enabling us to solve the wave equation, diffusion equation and Laplace equation in unbounded...

1. Let f(x, y, z) = x2 +y' and E = {(x, y, z) : 0 1. Let f (x, y, z) = :r2+y2 and E { (x, y, z): O .T,2 -+y2 S 4, y 2 0, O z f 3 Convert the integral J E f (x, y, z) dV into cylindrical coordinates...

Using source transformation, find i in the circuit of Fig. 10.94. 5 8 sin(200 30) A 1 mF

MDN, Inc. reports a net operating loss for 2021 of $4,864,000. Last year the company reported taxable income of $1,216,000 and in 2019 the company reported taxable income of $2,918,000. If the tax...

7. A dos inversionistas, en forma independiente, se les plantea la posibilidad de emprender un proyecto de inversin, que requiere de una inversin inicial de $1.000 y que arrojara los siguientes...

Required information [The following information applies to the questions displayed below.) The following partially completed process cost summary describes the July production activities of the...