1. Consider the model : Y = pYt-1+ Bo + Uz State all assumptions. (a) Derive the OLS estimator for p and Bo. (b) Derive E[e]. Is OLS biased ? (c) Derive E[bo]. Is OLS biased ?

Q: 1. (Review) (a) Suppose that X~ Cauchya and c> 0. Show that Y = CX ~ Cauchyca (Hint: This is a…

A: Given: X ~ Cauchya Thus, the PDF of X is given by: fX (x) = aπ.(a2 + x2)   for  x∈ℝ Now, the random…

Q: əz Use chain rule to find z = x² + 3wxy + w², with x = 2t + 1, y = et and w = 3 – t2.

A: The aim is to find, The formula for chain rule is,

Q: 1) (i) Find the gradient of f. (ii) Evaluate the gradient at the point P. f(r, y) = 12y-3 sin(y), P…

A:

Q: Calculate the energy coefficient from the first order if the infinite potential box is as uneasy as…

A: Given: φn=2LsinnπxLφ2=2∂Lsin2πx2L To find: Solution

Q: Exercise : Find dy O y = 1ox +3 Co sx Oy=cscxm4X+7 Catx 1+ Cotx

A: Note:- As per our guidelines, we'll answer the first three sub-parts of this problem. Please…

Q: 1 ^+x==? x = x

A:

Q: Let {B, :t>0} be the standard Brownian Motion, what's the value of E(B2|B1 = 1, B3 = 2)? Select one:…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Yt = €t – 0.5ɛt–1 + 0.5€t-2 Et ~ WN (0, 1) (a) Find E(y) and Var(y.). (b) Find Cor(yt, Yt–1) and…

A: We have to use definition of stationary time series.

Q: Exercise 2.3.2 Use whatever technology you have available to sketch a direction field for the given…

A: Direction field: A graphical representation of all the solutions of a first order differential…

Q: How do we find the linearization of g(x, y) = tan−1(xy2) at the point (1, 1). and use linearization…

A: To find the linearization of g(x,y)=tan−1⁡(xy2) at the point (1,1), we willl use the formula for the…

Q: Let Y have the pdf fy (y) = Let U e-Y. Find the pdf of U. = = e-y (1+e-y)2¹ -∞ <y<∞.

A:

Q: de Consider a model: = 1- cos 0 – ÷(1 + cos 0) dt (a) Determine the equilibrium points for this…

A: We are given, dθdt=1-cosθ -13(1+cos θ) Condition of Equilibrium: dθdt=0 ⇒1-cos θ-13(1+cos θ)=0⇒1-cos…

Q: 2. Given the functional equation (1 – s) = (27)¯³.2. cos (r(s)C(s). TS %3D Show that (s) = {(1 – s),…

A: Given ζ1-s=2π-s.2.cosπs2Γsζsand ξs=s1-sΓs2π-s2ζs

Q: Find the linearization of the function f(x) = ex at x = 0 where a is the center of the…

A: The given of the question is a function f(x)=ex, and the center of the linearization is a=0. The…

Q: Find the local linearization of f(I) = 1/1 at-3. %3D Ls(z) =U %3D

A:

Q: Consider the simple regression model t = 1,2,..., T where u̟₁ = pu̟-1 + & with |p] < 1 and E(&) = 0,…

A: Having first-order autoregressive (AR(1)) autocorrelation in the error term $u_t$ in a simple…

Q: consider the initial value problem (3,0227 y+25y=20,+7 410)=9.41(0)=0 1

A:

Q: Determine which of the given differentials is/are exact. In case it is exact, find the functions of…

A: For a given differential A dx +B dy +C dz Where A,B,C are function of x,y,z  will be exact if for…

Q: 6. f(t)=-e" sin (2r + 7) -2t 7. f(1)= 3e " cosh (In 21) %3D

A:

Q: 5. Determine whether the functions y, and y2 are linearly dependent on the interval (0,1). Yi = 1+…

A: Linearly independent of the function. Using Wronskian

Q: of the function f(x) =e* the value of e 0.2 2. Use the linearization at a=0 to approximate

A:

Q: Use integration by parts twice to evaluate fet cos(3t)dt: Step 1: Let u = et and du + S fet…

A:

Q: Let u(t) = (3,3t,t) and v(t) = (3t, - 2t,2). Compute the derivative of the following function. u(t)…

A:

Q: Q.8 Find the gradient Vw ofthe function w = In /x² + y² + z². %3D

A: Given function W=ln(√(x2+y2+z2)) Now we will find the gradient as shown below

Q: What is the rule used to transform ΔABC to its image?A(−3, 5), B(2, 8), C(−4, −5) and A'(−3, −5),…

A: The objective of the question is to identify the transformation rule that was used to transform…

Q: 1) Find the equilibra and sketch the phase line of the autonomous ODE u' = u*(2 – u). Determine the…

A:

Q: dz/dt = -Bz(1 – vz), z(0) = 1. %3D

A: