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 normal equations? 2) Find the conditional inverse 3) Whether the parameter B0 and ß1 are estimable? Prove that! 4) Prove that (B1 – B2) is estimable

Q: If u = x+ 1 t = vu y = t? then, = 0 dy dx dy 2. = x dx dy 3. = 1 dx dy dx 1. 4.

A: (3) We have to find out dydx

Q: 5 - If f(x) = За and the equation of the normal line to the curve at the point (a, b) is x + 2a y =…

A: The objective is to the find  the value of equation a+b-c=?. We are given that the equation of…

Q: 18.8. (a). Let y be the contour z = e", - TOST traversed in the %3D positive direction. Show that,…

A: To solve the given question we shall use the following formula: Cauchy integral Formula: Let C be a…

Q: Exercise 2. Prove that dim(null T") = dim(null T) + dim W – dim V and dim(range T") = dim(range T),…

A: We prove dim null T*=dim null T + dim W-dim V and dim range T *=dim range T for every T L(V·W).

Q: Let X=(1,0, – 1, -/2)'. Then, ||X||=v2 Select one: True False

A:

Q: 5. Deduce the standard linear approximation of 1 x2+y2+z2 at Po(1,2,3).

A: The general formula of the standard linear approximation for f(x,y,z) is generally given by,…

Q: Q1 Let X1,.,X, f(r;0) = )0"(1 - 0)2-,x = 0,1,2. (i) Find the score and information functions of 0.…

A: Let, X1,x2,...,Xn be the random samples having following distribution: f(x;θ)=2xθx(1-θ)2-x  ;…

Q: 4.) x : 12 required:a) find the value of x if y = 1/2

A: Given, x=-112y142y-y214We need to find value of x when y = 12

Q: Find an equation of the normal line to the parabola y = x² - 8x + 4 that is parallel to the line x -…

A:

Q: 8. Find all values of h, if any exist, such that b a linear combination of vị an h (а) Vi V2 = b =…

A:

Q: 2. Show that for simple linear regression (SLR) we have that cov(B, B,) = - xoʻ/S

A:

Q: 3 0 -2 3-Let A= 0 1 2, B= Find:- 3 L-1 1 5] (2A – I)B' and show that (BA)'=A'B'

A:

Q: If F(x²_ye, ye-z?) = o then Prove that + XZ Z 2Z · Rx =

A: Given Fx2−y2,y2−z2=0 We have to show that yz∂z∂x+xz∂z∂y=xy The function Fx2−y2,y2−z2=0 can be…

Q: Show that the following relationships hold. a) (1+i)™sn[ = Sn+m[ ¯ Sm| b) än+1] = 1+ an] (m) (m), c)…

A: Considering the LHS (Left hand Side) : LHS=(1+i)mSn|¯ RHS=Sn+m|¯-Sm|¯ ( Right Hand Side)…

Q: Q4. (a) Give A = 2xy â, +3â, +z'yâ,, calculate v.AdV as shown in Figure Q4(a). A, (0, 1, 1) (0,0, 1)…

A:

Q: 6. The first four central moments are 0.4, 8 and 144. Find 'B' and 'y' coefficients?

A:

Q: b) Find f(")(x) is S(x) =

A:

Q: 3. Show that S4 has the presentation (x, y|x* = y² = (xy) = 1). %3D

A: To show: S4 has the presentation x,y| x4=y2=(xy)3=1

Q: 8) The relationship between the TSLS slope and the corresponding population parameter is: (Z; - Zju;…

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

Q: 11.(b) The relationships between 0, B, 0 and ß implied by the model assumptions are: * a. 0= 0 and B…

A:

Q: Consider the function f(x) = r³ + 5 x² + 3. Find the equation of the normal line at the point (1,…

A: Given function is, fx=x3+5x2+3 To find the equation of the normal line at the point (1,9).

Q: W = 0.3RX +0.7Ry, where Rx is the stock return from investing in stock X and Ry is the sto investing…

A:

Q: Find the maximum and minimum values of the ratio x’A x/x'x for any nonzero vectors x' = [x1, x2, X3)…

A: We have to find maximum and minimum value of ratio x'Ax/x'x

Q: 2-Prove that: B (m, n)-ß (a,m) 3- Simplify to the simplest: (2+0(1-0) (1+0)(3-2)

A:

Q: Q. Two: For a random process X(t) with E(x2(t)) = sin(t) we have Pxx = %3D %3D A) 0 B) 1 С) 2 D) 3…

A: Given that, for a random process Xt,  EX2t=sin t

Q: Q4) Find the result of the following: 1. i¹ = ? 2. B (125/50, 1) =? (Beta function) 3. Given z/= (4…

A:

Q: What is the equation of the normal line of f(x) = ln(x² – 3) at the point x = 2 ? %3D

A: Given:fx=lnx2-3  at a point x=2

Q: Find the tangent plane and normal line to In X 2y = z²(x-2y) + 3z +3 at (4, 2, -1).

A: