A natural cubic spline S is defined by S0(x) = 1+B(x −1)−D(x −1)3, if 1 ≤ x < 2 S1(x) = 1+b(x−2) −3/4(x−2)2 + d(x−2)3, if 2 ≤ x ≤ 3 If S interpolates the data (1, 1), (2, 1), and (3, 0), find B, D, b, and d.

Q: Show that Y parameter 8. (X₁+2X₂ +3X3) is not a sufficient estimator of the Bernoulli

A: Y=1/6(X1+2X2+3X3) is not sufficient estimator of the Bernoulli parameter

Q: 3. (2.6.7) Use Horner's method to calculate g(-2) and g/(-2) where g(z) = 42¹-52³+ 6-7. Do not use a…

A:

Q: The critical points of the function f(x) = 5x² – 6x + 12 are %3D

A: A critical point of a function of a single real variable, f(x), is a value x0 in the domain of f…

Q: Q4. In simulation study of a manufacturing system, both the average daily production rates obtained…

A: Given information: Consider the given dataset: Actual Production Rate Simulation Result 432 444…

Q: 1,3 2,1 3,4 f(x) 2,6 3,5 3,2

A: The given tabular data is,

Q: Adam's value function is V(x) =, for gains (X 2 0) and (x) = - 3/Tx| for losses (X<0). Adam is…

A: Winning Utility Function V(x) = x4 Losing Utility Function V(x) = -3|x| Expected utility from the…

Q: 24. Differentiate each of the following with respect to x. Simplify fully when indicated 1 (a)_y=x²³…

A:

Q: If T, is an MVUE of y (0) and T, is any other unbiased estimator of y (0) with efficiency e < 1,…

A: Answer: For the given data,

Q: D) Identify the even function among the following. A) f(x) = 2|x| - x² %3D B) h (x) = 2x – x² %3D C)…

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Q: Linearize x³ + ln x about x=3

A: Let f(x)=x3+ln x about x=3 f'(x)=3x2+1x Recall: Linearization  L(x)=f(a)+f'(a)(x-a)  we have a=3

Q: 1. Linearize x³ + ln x about x=3 In

A: Given: Linearize x3+ln x about x=3 To find: To find the linearization of x3+ln x about the point x=3…

Q: Find the general solution of the given differential equation. 9y" - 4y = 0 y(t)

A:

Q: 16. As a generalized interpolation problem, find the quadratic polynomial q(x) for which q(0) = -1,…

A: let the polynomial q(x)=ax2+bx+c q'(x)=2ax+b since q(0)=-1(given) a(0)+b(0)+c=-1⇒c=-1

Q: Which of the following functions when evaluated at g(v2) gives a value of 9/2? g(x) = x° – 2)2 x2…

A: Put value in given function and check

Q: In the context of ordinary least square (OLS): Given mịn- ||Y – Xß||? Use derivatives to derive the…

A:

Q: 5. Let X₁, X2,..., Xn be iid N(A, A²), A > 0. For this model both X and cS are unbiased √n - II ((n…

A: Let X1, X2, .......Xn be independent and identically distributed with the normal distribution of…

Q: 1.1 Let u(x; y) = 4(x2 - y2 ) - 5y. If f(x; y) = u(x; y) + iv(x; y) is an entire function, then v(x;…

A: Let u(x; y) = 4(x2 - y2 ) - 5y. If f(x; y) = u(x; y) + iv(x; y) is an entire function, then v(x; y)…

Q: If (1,7) is both a critical point and a point of inflection for the function 3 2 f(x)=x²- cx² - 3dx²…

A: fx=x4-cx3-3dx2+5x+5

Q: 3. Consider the functions, m(x) = x + 3x and p(x) = 2x + 5, Find m(p(1)) b. Find m(p(x)) a. c. Find…

A:

Q: 20.) Find the linearization, L(x) ,of f(x)=x*+3x² values of f(x) when x=-1 , x=-1.1, x=-1.5 , and…

A:

Q: (a) Develop f (x – 4h), f (x + 3h), ƒ (x) and ƒ (x+ 4h). a first-order method for approximating f"…

A:

Q: Find f(k-1) when f(x) = 5x² + 3x + 6. OA. f(k-1)= -7K² +5k+8 OB. f(k-1)=5k2-7K+8 OC. f(k-1)=5k²-7k+…

A: Given,

Q: 4. The following function f(x) = { 1²,1≤0 -²,0 ≤ ≤1 1-2x, 1≤x

A: Definition is given below.

Q: 2. Suppose that f(4) = 2, g(4) = 5, f/(4) = 6, and g/(4) = -3. Find h/(4). a. h(x) = f(x)g(x) b.…

A:

Q: The graph of y = 8x - x² and the line y = 7 for 0 ≤ x ≤ 7 is shown. 18 16 14 12 10 8 6 4 2 0- -1…

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Q: Q1) A) Whether the function is even, odd, or neither. 1) h(x)= 2x +1 2) k(x) = x³ +x B) Find the…

A: See the attachment

Q: Calculate M6 for f(x) = √7x on [0,2]

A:

Q: Which variables is/are included in the best set of the model using backward elimination?  a. x1 b.…

A: From the above output we can see that the p-value for variable X2 is 0.074. which is greater than…

Q: 1. Let f(x,y)=x²y + √y Find each value a.f(2,1).b.f(3,0).c.f(1,4)

A: We have to find the value of the function for the given points, f(x,y) = x2y + y points : f(2,1)…

Q: (iv) p(39), where p is the Euler p-function.

A: Euler totient function and residue classes

Q: 27. A rectangular field is to be enclosed with 200 meters of fence. Which of the following models…

A: Area of rectangle is given by Area of rectangle=l×w Here l and w is length and width of rectangle…

Q: 12. Let f(x) = x + 2 and g(x) = x² - 1. Find (gᵒf)(4)

A: Given two functions 1.f(x)=x+2 g(x)=x^2-1 lets find g(f(x)) at 4

Q: 5. Given f(x) = Vx – 3 and g(x) = 3x* – x? + 2, find %3D a) (f•g)(x) b) g(F(x)) = Domain:

A: