Let (X₁, X₂) be a pair of standard exponential random variables with the countermonotonicitycopula and let U be a standard uniform random variable.a) Find a stochastic representation of the form (X₁, X₂) = (f(U), g(U)) for functions f and gwhich shows how (X₁, X2) can be simulated.b) With the help of a), use software and numerical integration to calculate the minimalcorrelation for two standard exponential random variables.

Given: Let (X₁, X₂) be a pair of standard exponential random variables with the countermonotonicity…

Answered: Let (X₁, X₂) be a pair of standard…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Heteroscedasticity Stigler and Friedland (1983) conducted a study to determine whether the separation of company control from company ownership affects company profits. Using data from 69 companies in the United States, the authors estimate the following model: profiti = α + β1asseti + β2management_controli + ei Where i is company and: profiti = annual profit (in million dollar) asseti = company asset (in million dollar) management_controli = dummy variable that is worth one if the control of the company is held by the manager The regression results are presented in the table in the picture a. Explain whether the statements below are TRUE, FALSE, or CANNOT BE DETERMINED. "If there is a heteroscedasticity problem, the confidence interval of the OLS estimator is not valid." b. Determine the 95% confidence interval for the parameter 2, what can you conclude?
Consider an MA(1) model and suppose we have the observed values Y₁ = 0, Y₂ = −1, and Y3 = 1/3. Find the conditional least squares estimator of 0 and the method of moments estimator of σ².
An electrical system consists of 2 components (C1 and C2) functioning independently and are set in a serial layout. The failure time of each component follows an exponential distribution with rate 2 in every year. Thus the system will operate if both components function, and itwill fail if any one component fails.(a) Obtain the failure density and distribution of the system(b) Obtain the survival function/distribution of the system.(c) Based on your answer in (a) and (b), calculatei) the probability that the system fails in less than 8 months.ii) the expected time to failure of the system.
Consider the SIR model from the topics videos with parameters: B = 1.6875, y = 0.75, and N = 4. Assume the system is in state X (t) = (3,1). %3D (a) What is the rate of the infection event? Number (b) What is the probability that the next event is a recovery? Number
If λ = 6 per hour and μ = 6 per hour in an (M/M/1): (5/FIFO) model, find the probability that there is no customer in the system.
Consider the least squares problem Ax=b, where 1 0 A = - (2) ¹ - () and b 1 (a) Write down the corresponding normal equations. (b) Determine the set of least squares solutions to the problem. (c) Let H = col(A) be the column space of A. Find the best approximation of b in H.
Example 18.2 For the probability density of a system of random variables (X, Y): f(x, y) = 0.5 sin (x + y) (0 < x < 7,0 << 7), 2' determine (a) the distribution function of the system, (b) the expectations of X and Y, (c) the covariance matrix.
For a GLM with canonical link function, explain how the likelihood equations imply that the residual vector e = (y – @) is orthogonal with C(X).
Linear regression aims to fit the parameters based on the training set D = {(x(i),y(i)), i = 1,2,..., m} so that the hypothesis function ho (x) 6T.x = 00+ 01x₁ + 0₂x₂+......+ Onxn can better predict the output y of a new input vector x. Please derive the stochastic gradient descent update rule which can update o repeatedly to minimize the least squares cost function (). =
Derive the normal equations for the least-squares cubic f(x) =Ax 3+ Bx 2+ Cx + D.

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