Homework Answers
Add Answer to:
1. Consider the following linear model y Xp+ €, where Cor(e)-021 with ơ e R+ being unknown. an estimable function, where C is a full column rank matrix of rank s. Let T'y be the Let C. β BLUE...
Suppose we have the full rank linear model y = XA+ Ewiun xp design matrix X,...
Suppose we have the full rank linear model y = XA+ Ewiun xp design matrix X, normal errors E N (0,0?Inxn). Let b be the least squares estimator of B. (C) Prove that (b-B)? XT X(6-8) o2 follows the x? distribution. Hint: Write Xb in terms of X, B and e. (d) Hence derive a 100(1 - a)% joint confidence region of ß given in notes (b - B) TXTX(b-)/po<Fa:pon-p, where Faip,n-p denotes the upper ath quantile of the Fpin-p...
in a Bayesian view. Consider the prior π(a)-1 for all a e R Consider a Gaussian linear model Y = aX+ E Determine whether each of the following statements is true or false. π(a) a uniform prior. (1) (...
in a Bayesian view. Consider the prior π(a)-1 for all a e R Consider a Gaussian linear model Y = aX+ E Determine whether each of the following statements is true or false. π(a) a uniform prior. (1) (a) True (b) False L(Y=y14=a,X=x) (2) π(a) is a jeffreys prior when we consider the likelihood (where we assume xis known) (a) True (b)False Y-XB+ σε where ε E R" is a random vector with Consider a linear regression model E[ε1-0, E[eErJ-1....
(b) . Write the k-th step of the trapezoidal method as a root-finding problem Ğ = is Y+1 where the unknown (e)Find the Jacobian matrix of the vector function from the previous part. (dWrite a funct...
(b) . Write the k-th step of the trapezoidal method as a root-finding problem Ğ = is Y+1 where the unknown (e)Find the Jacobian matrix of the vector function from the previous part. (dWrite a function in its own file with definition [Y] dampedPendulum(L, T) function alpha, beta, d, h, that approximates the solution to the equivalent system you derived in part (a) with L: the length of the pendulum string alpha: the initial displacement beta: the initial velocity d:...
Exercise 1 Answer the following questions: a. Consider the multiple regression model y-Xe subject to a set of linear constraints of the form Cß-γ, where C is mx (k + 1) matrix. The Gauss-Markov condi...
Exercise 1 Answer the following questions: a. Consider the multiple regression model y-Xe subject to a set of linear constraints of the form Cß-γ, where C is mx (k + 1) matrix. The Gauss-Markov conditions hold and also ε ~ N(0, σ21) Is it true that we can test the hypothesis C9-γ using a k¿SSRfillm d SKreducedmodel Please explain b. Refer to question (a). Let H and Hi be the hat matrices of the full and reduced model respectively. Show...
() At)x()B(f)u() Consider the following time-varying system y(t) C(f)x(t) where x) R", u(t)E R R 1...
() At)x()B(f)u() Consider the following time-varying system y(t) C(f)x(t) where x) R", u(t)E R R 1 1) Derive the state transition matrix D(t,r) when A(f) = 0 0 sint 2) Assume that x(to) = x0 is given and u(f) is known in the interval [to, 4] Based on these assumptions, derive the complete solution by using the state transition matrix D(f, r). Also show that the solution is unique in the interval [to, 4]. 3) Let x(1) 0 and u(f)...
Suppose we have the full rank linear model y = XA+ Ewiun xp design matrix X, normal errors E N (0,0?Inxn). Let b be the least squares estimator of B. (C) Prove that (b-B)? XT X(6-8) o2 follows the x? distribution. Hint: Write Xb in terms of X, B and e. (d) Hence derive a 100(1 - a)% joint confidence region of ß given in notes (b - B) TXTX(b-)/po<Fa:pon-p, where Faip,n-p denotes the upper ath quantile of the Fpin-p...
in a Bayesian view. Consider the prior π(a)-1 for all a e R Consider a Gaussian linear model Y = aX+ E Determine whether each of the following statements is true or false. π(a) a uniform prior. (1) (a) True (b) False L(Y=y14=a,X=x) (2) π(a) is a jeffreys prior when we consider the likelihood (where we assume xis known) (a) True (b)False Y-XB+ σε where ε E R" is a random vector with Consider a linear regression model E[ε1-0, E[eErJ-1....
(b) . Write the k-th step of the trapezoidal method as a root-finding problem Ğ = is Y+1 where the unknown (e)Find the Jacobian matrix of the vector function from the previous part. (dWrite a function in its own file with definition [Y] dampedPendulum(L, T) function alpha, beta, d, h, that approximates the solution to the equivalent system you derived in part (a) with L: the length of the pendulum string alpha: the initial displacement beta: the initial velocity d:...
Exercise 1 Answer the following questions: a. Consider the multiple regression model y-Xe subject to a set of linear constraints of the form Cß-γ, where C is mx (k + 1) matrix. The Gauss-Markov conditions hold and also ε ~ N(0, σ21) Is it true that we can test the hypothesis C9-γ using a k¿SSRfillm d SKreducedmodel Please explain b. Refer to question (a). Let H and Hi be the hat matrices of the full and reduced model respectively. Show...
() At)x()B(f)u() Consider the following time-varying system y(t) C(f)x(t) where x) R", u(t)E R R 1 1) Derive the state transition matrix D(t,r) when A(f) = 0 0 sint 2) Assume that x(to) = x0 is given and u(f) is known in the interval [to, 4] Based on these assumptions, derive the complete solution by using the state transition matrix D(f, r). Also show that the solution is unique in the interval [to, 4]. 3) Let x(1) 0 and u(f)...
Most questions answered within 3 hours.
-
1.A solution has a pH of 5.5. What would be the color of the
solution if...
asked 13 minutes ago -
Over time, hydrogen peroxide, H2O2,
degrades into water and oxygen gas. A bottle of hydrogen
peroxide is...
asked 8 minutes ago -
2. Consider the following data table for a hypothetical
economy.
Aggregate
Consumption
Personal
&n
asked 12 minutes ago -
Adidas Runs Into Supply-Chain Problems in Crucial North
American Market
Shares fall amid concern the sporting-goods...
asked 14 minutes ago -
The physical plant at the main campus of a large state
university recieves daily requests to...
asked 52 minutes ago -
Determine the probability p(2) for a binomial
experiment with n=12 trials and the success probability
p=0.1....
asked 25 minutes ago -
What is the vapor pressure at 20 degrees C of an ideal solution
prepared by the...
asked 23 minutes ago -
You want to find the independent and dependent variables taken
from a sample of 30 dropouts....
asked 56 minutes ago -
. A light signal is traveling through a fiber. What is the delay
in the signal...
asked 45 minutes ago -
“Architects can have an important and direct impact on thermal
comfort and IAQ for improving design...
asked 28 minutes ago -
A 1.10 kg sample of a metal sample absorbs 43.5 kJ of heat,
resulting in a...
asked 52 minutes ago -
Many pharmaceutical compounds contain amine functional groups,
as they are adapted from amine-containing alkaloids. These drugs...
asked 32 minutes ago