Consider the econometric model y = Bo + B1x +u and the OLS estimator B, for B1. We know that: O Var(ŝ1) = Var(Bo) O Var(31) = E[ŝ, - Bi]² O Var(§1) = E[§,]² O Var(B,) = Var(u) if we assume homoskedasticity

Q: Example 8.10. Evaluate by using (i) Trapezoidal rule, 1+ (ii) Simpson's 1/3 rule, (iii) Simpson's…

A: To evaluate ∫06dx1+x2 Using  (i) Trapezoidal rule (ii) Simpson's 1/3 Rule (iii) Simpson's 3/8 Rule.…

Q: Suppose that {Y(t), 0 0|Y(1/2) = 0) × .9213. %3D

A: Given information: {Yt, 0≤t≤1} is a Brownian motion process with variance parameter σ2.

Q: Exercise 3: Suppose that in an electric display sign there are three light bulbs in the first row…

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Q: Find the elgenpairs of matrix A and the vector Kty such that the initial vahue problem * = Ax, x(0)…

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Q: 1. We start from the model Y = Xß + u for which what we have called hypotheses are fulfilled ideals.…

A: The given model is Y=Xβ+u. The answer is given using the concept of OLS and Random perturbations.

Q: 2- An insulated rod of length 30 cm has its ends A and B kept at 20•C and 80•C respectively until…

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Q: Suppose Y; = B1x; + €;, i = 1, ...,n. In this equation x is non-random, ß1 is a parameter (unknown…

A: Hello! As you have posted 4 different questions, we are answering the first question. In case you…

Q: 3) Consider the autonomous DE: y' = y² + 3y - 10 A) Find the critical points of the given DE.

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Q: 5- The equation (y`-y =e2x ) is : ( linear, exact, separable, Bernoulli )

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Q: Exercise 3: Suppose that in an electric display sign there are three light bulbs in the first row…

A: As student want answer of only part 3,  So, I am providing the answer for that part only.

Q: a) Suppose that {X,,t=0,±1,±2,....} is a stationary process satisfying the equations X, = 4X,-1…

A: Please find the explanation below. Thank you.

Q: Consider the linear model Y₁ = B₁ + B₁X₁¡ + ß₂X2i + u; where u; is the error term and where E (u;…

A: 4 main assumptions of Gauss Markov multiple linear model are : Linearity : The errors and…

Q: Find a particular solution to y" + 5y' + 6y = lte".

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Q: find the critical points for dA=2A=0.01 AL and dL/dt=-0.5L+0.0001AL

A: Critical points are the points in a graph, at which the direction of graph changes.

Q: Theorem 17-1. If T, is a consistent estimator of y(0) and y {y(0)} is a continuous function of y(0),…

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Q: 5. Apply the Euler-Cauchy method with step length h to the problem y'=-y, y(0)=1 h = 0.1

A: y' = -y , y(0)=1 and h=0.1 f(x,y) = y' = -y  x0 = 0   and  y0 = 1

Q: a. Suppose Y; = B1x; + €;, i = 1, ..., n. In this equation x is non-random, B1 is a parameter…

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Q: The joint pmf of X and Y is f(x, y) = 1/6, 0 ≤ x+y ≤ 2, where x and y are nonnegative integers.…

A: Joint pdf of X & Y is        f(x,y)=1/6;  0≤x+y≤2, x,y>00  ; elsewhere Marginal pdf of X is…

Q: log, x = 5.3 and log3 y = 2.1, %3D log4 u = 3.2 and log4 v = 1.3. 19. log3 (9xy) 27. log3 (x²y³) 20.…

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Q: Exercise 7.9 The model is Y = Xß + e with E (e | X] = 0 and X € R. Consider the two estimators (b)…

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Q: Assuming a Gamma mixture model and using Ez [In p(X, Z)|X, Oʻ]. which of the following is the update…

A: Gamma Distribution:              Basically, Maxiture model is widely used in the…

Q: The bivariate beta type I pdf is fx,„x, (x1, x2) = Kx-x" (1 – x1 – x2)e-!, x1 > 0, x2 > 0 and x1 +…

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Q: Consider the equilibrium O of the continuous-time system given by å = Ax,where A E R²×". Which of…

A: This is a problem of the Dynamical system, a system of the differential equations.

Q: The maximal altitude of a satellite is given by the formula Y = yo + (R+ yo) + yo) [211 + 1 - 1]. -…

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Q: To find a particular solution of the form Yp = U1y1 +U2y2 of a nonhomogeneous DE using the variation…

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Q: Find the general solution of the Cauchy-Euler equation: X^3y’’’ - x^2y’’ + 2xy’ - 2y = x^3

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Q: Let z, be the observed stock price at time t Which of the following model(s) is AR(p) model? Az, = a…

A: The answer to the above question is as follows :

Q: In a bivariate regression model x; = do + 812i + fi, if cov(z, E) = 0 and E[E|2] = 0, then the OLS…

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Q: Consider a logistic regression system with two features x1 and x2. Suppose 00 = 5, 01 = 0, 02= 0,…

A: In logistic regression, the hypothesis function hθx is a sigmoid function which returns the values…

Q: 1 Find the Nahee af the falloding in togreals's Jet X+1 3. 8. +3. -4+3 da -2 2 JX -9. 2. Lett-lx 9.…

A: You don't mention which question i have to solve. And you already solved them. I go through all the…

Q: 1. Find the orthogonal trajectories of the family of curve a+3y2 = cy ,where c is an arbitrary…

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Q: 4. Suppose that for a particular linear model [2 1 X'X = 1 li 0 1l [14] X'y =| 6 1] 1 8 1) What the…

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Q: Let µ(x)= e8x" be the standard integrating factor to x y' +p(x) y = x³. Find p(6).

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Q: 2. Show that the substitution z=y(1-n) will reduce the Bernoulli Equation y' + f(x)y = Q(x)yn to a…

A: The solution is given as

Q: 11.Given Y = µ+ pYt-1+ Ut +a Ut-1 Where ut is the white noise process. a. Define the weak stationary…

A: The time series is the sequence of observations that observed in chronological order.

Q: Use the graphical approach to classify the following Lotka-Volterra models of interspecific…

A: Given system is dN1dt=6N11-N113-0.1N213dN2dt=4N21-N235-0.2N135

Q: 1)Show that the forward Euler method applied to the following IVP is stable: y' = 2y – t, y(0) = 1.…

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Q: 12. Suppose an enzyme is known to obey Michaelis-Menten kinetics, but the parameters V and K are not…

A: Given:-             Suppose an enzyme is known to obey Michaeli's-Menten kinetics, but the…

Q: Find the general solution of the following linear second order inhomogeneous O.D.E.: ý - y = e*

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Q: Let X1,..., Xn be iid and U([a, b])-distributed with unknown parameters 01 (a) Use the method of…

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Q: What are the equilibrium solutions of the DE dy/dt=4ty−t? If there is more than one, list all of…

A: Given differential equation is  dydt=4ty-t             (i) Equilibrium solution of the system can be…

Q: 3. Find the general solution to the second order nonhomogeneous linear equa- tion y" +y/ - 2y = 6et.

A: To find the particular solution use the method of undetermined coefficients. Since e^t appears in…

Q: Q1: Let X have p.d.f ==,x = 1,2,3 and X, and X2 are stochastically independent. Let Y1 = X,X2 and…

A: Given Information: Let X have pdf; fx=x6; x=1,2,3 X1 and X2 are stochastically independent. Y1= X1X2…

Q: Consider a simple linear regression model Y = Bi + B2X + e with E[e|X] = 0. Let b1, b2 be the…

A: For the given statement, we know that Homoskedasticity holds but e is not normally distributed then…

Q: Problem X(t) is a stationary Gaussian random process with ux(t) = 0 and autocorrelation function…

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Q: 2. Consider a stationary AR(2) process y = 0.6y-1 + 0.3y-2 + 8, where &- WN(0, 4). a. Find the mean…

A: 1) mean= 5 variance=2 2)ACF is an (c o mplete) auto-correlation function which gives us values of…

Q: An industrial concern has experimented with several different mixtures of the four…

A: Step 1 From the given data we get following table, SN Mixture 1 Mixture 2 Difference…

Q: Theorem 17-6. If T, is an MVUE of y(0) and T2 is any other unbiased estimator of y(9) with…

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Q: a) Show that the fourth-order Runge-Kutta method, k₁ = hf (ti, wi), h k₁ k₂= hfti+ Wi + 1/12) 2' h…

A: Given:  k1=hfti, wik2=hfti+h2, wi+k12k3=hfti+h2, wi+k22k4=hfti+h, wi+k3 and wi+1=wi+16k1+2k2+2k3+k4…