. Find a norm on R2 for which ||(0, 1)|| = 1 = ||(1,0)|| and for which |(1, 1)|| = 0.000001. %3D (Hint: try ||(a, b)|| = Ala + b| + Bla - 6|.) %3D

Q: Use the Error Bound to find a valve of N for which Error CSN)<1 x 10-9. is 1.5 3x

A: Error bound for Simpson's rule is defined as follows.  For a function fx, if  f4x≤M, then…

Q: 2. (i) Show that for a discrete dis.ribution B2> 1. (ii) Show that B2> B1

A:

Q: 4.3.a Use Theorem 9.4 to show that Y is sufficient for p 4.3.b Find the MVUE for p

A:

Q: Let G = Z31, S = {1,5, 6, 25, 26, 30}. %3D %3D Prove that Cay(G, S') is normal.

A: It is given that

Q: Grplain why Ž diverges, 27 41 even though has a finite liniit 2 t 2

A:

Q: Let X N (u,1) of size n. Obtain UMVUE for M.

A: We will use Lehmann-Scheffe theorem to find the uniformly minimum variance unbiased estimator for μ.

Q: Find diagonal matriy D is similar with A a A = [3 8-5

A:

Q: Show that the Stein operator for Poisson P(Y = k) = is Tf(r) = Af(k + 1) – kf(k).

A: Given information: The Stein operator for Poisson P(Y = k) = λk/k! is Tµf(x) = λf(k + 1) – kf(k).

Q: A cubic spline S is defined by: So(x) = 3(x- 1) + 2(x – 1)² – (x – 1) S(x) = s,(x) = 4 + 4(x – 2) –…

A: Natural Cubic Spline is a piece-wise cubic polynomial that is twice continuously differentiable.…

Q: Use the following rule in mathematical morphology to fill the holes inside the image A to be black.…

A:

Q: Q4/Find Loplace transtorm of £(4)= et by using} defining fanotion ر م ) ) st e" dt

A:

Q: 2) Determine the dimension of Null A and Col A for the marix 1 2 30 0] A =0 0 1 0 1 0 0 0 1 0

A:

Q: Find and plot the cubic spline S satisfying S(0) = 1, S(1) = 3, S(2) = 3, S(3) = 4, S(4) = 2 and…

A: %File Name: findSplineCoefficient.m %Define function function [ retCoeff ] =…

Q: Find the dimensions of the minimum-cost open-top rectangular tainer. (Let v* = 10 m³.) con-

A: Given. We need to find the dimension of a topless cuboidal container. Whose volume is 10m³ And…

Q: det TiP M,2 be defined by -Q,X + QX + agX ). Show that ī is a linear transforimation and find T…

A: The solution is given as

Q: How many rows and columns must a matrix A have in order to define a mapping from R4 to R6 by the…

A: Given: A mapping from R4 to R6 by T(x)=Ax Find how many rows and columns having the matrix A

Q: Suppose N E L(C) is nilpotent and has a Jordan form with only one Jordan block. Describe a Jordan…

A: According to the given information,

Q: Q:3 If sequences (xn)&(yn) are both in normed space X and Xn - x & yn →y, then x, + Yn x + y.

A:

Q: 8. Let C be the perimeter of the square with vertices at the points z = z = 1+i, and z = i traversed…

A:

Q: 15) o veclovs ú = Givetw and Tñ=211 deternine the projection d on 2.

A: This question can be solved using the projection formula.

Q: Q1. Compute xdx x'+10 using trapezoidal and Simpson's 1/3 rules with the number of points 3 and 5.

A: The given integral is, I=∫01xdxx3+10 Dividing the interval (0,1)  into 2 intervals (for 3 points)…

Q: My question is why is norm defined like this please explain 2 | U | Le() = inf 1B>0:√ [(x) [P(x) do…

A:

Q: defined BCX,x). a norm Dn

A:

Q: (b) If X is a normed line- ball M= {xeX:x≤1}

A:

Q: 12) Find the clamped cubic spline for the data (1,1),(3,4), using that f'(1) = 2, f'(3) = 5

A:

Q: X1,, Xn ~ N(-3,2) (random variables) ... Z, = 1(X,X2 + X1X3 + X1X4 + •..+ X1X„), n > 3 %3D (a) Find…

A: From the given information, X1, .....,Xn~N-3,2 And Zn=1nX1X2+X1X3+...+X1Xn, n≥3 Consider,…

Q: The Wronskian of y,(t)=e 2, y,()=e" is-e St. Select one: True False

A:

Q: 1. Let k -k x = VE Find the Euclidean norm of x. Don't assume any specific value for k. So, the…

A: Since not a particular question asked, as per guidelines solution to only first question(Q1) is…

Q: Where x = (X1, X2) E R². 3- N: R2 - → R defined by N(x) = /x1² + x2² is a norm on R². (x1, x2) E R².…

A: Let X=(x1,X2)€R^2

Q: az Find if yz – In z = x + y ax 3.

A: We have              yz-lnZ=x+y

Q: Prove that Z(Sn) = {e} for n ≥ 3.

A:

Q: 4. Evaluate the Kullback-Leibler divergence between two Gaussians p(x) = N(xu, E) and %3D q(x) =…

A:

Q: A natural cubic spline S on [0,2] is defined by (So(x) = 1+ 2x – x³ S(x) = Is, (x) = a + b(x – 1) +…

A: Given: Natural cubic spline S on [0,2] is defined as: Sx=S0x=1+2x−x3 if 0≤x≤1S1x=a+bx−1+cx−12+dx−13…

Q: d the integration norm of the giver x) = -9x + 2

A: In this question we will use basic of calculus i.e integration. We will simply integrate the given…

Q: Recall that for D a squarefree integer, the norm function N on Q[VD] is defined by N(a + bVD) = (a +…

A:

Q: Find a norm of the function f(t) =t – 2t in space L10, 1] 1 a. 6 С. е. d. ai

A: We use the definition of norm in L1[0,1] to answer the given question.

Q: Find a norm of the function flt)= t+2t in space C^co13 %3D where normis given by formula ms x…

A:

Q: Q1. Compute xdx x' +10 using trapezoidal and Simpson's 1/3 rules with the number of points 3 and 5.

A: we have  I=∫01x dxx3+10dx  n=3h=b-an=1-03=13…

Q: A cubic spline S is defined by: (So(x)%D 1+x- x (5,(x) = 2 - 5(x – 1) + (x – 2) if 0 SxS1 if 15xS2…

A: As we all know that Natural Cubic Spline is a piece-wise cubic polynomial that is twice continuously…

Q: For p = (1, 0) and x = (x₁,x2,...,xn) ER", define ||2|p:= - ². |P Show that n jyjx|py|q for x, y…

A:

Q: Find the charecteristic yfalynemicl matrin g the fellewing 3 -2 e 2

A: the given matrix is: 400532-202 we have to find the characteristic polynomial of the given matrix.

Q: A) If o0, then : w(8)s (+d) W(8).

A: A) Let fx be a continuous function on a,b then for δ&gt;0 wδ=supfx1-fx2 ∀x1,x2∈a,b s.t x1-x2&lt;δ…

Q: 5. Which of the following statement(s) is/are TRUE about the Jacobi and Gauss-Seidel methods ?

A: For the given methods, statements II and IV hold true.

Q: Find a norm of the function f(t) = 2t4 – tin space C0, 1], where norm is given by formula max|f(t)|…

A:

Q: Determine wheter f and are înverses (43) F(x)= XHb gle) =

A:

Q: Assume C and D are chosen at random from {1,2...,n}. Let pn be the probability that C + D is a…

A: The number of pairs (c,d)  with sum m2 is m2-1 for m2≤n and 2n-m2+1 for n&lt;m2&lt;2n. Hence,…

Q: Question 2: Show that the set S = {rVT + V2:rE Q) is dense in IR. Explain and show your work.

A:

Q: Find the area of the inner loop of r = 3 + 4cose.

A: