Consider the following problem max f (x) =Σxjn( i=1 subject to x, =1 i=1 2(i-1)x,= (n- 1)d i=1 *, E [0, 1]

Q: • Let X1,...,Xn iid Poisson (0) such that E(X1) = 0. Suppose that Find the level a = 0.05 LRT for…

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Q: EXERCISE 1. Find equation 2. For the E different- Xフ5 -h (x 5oɔ 9-T)(XUIS h+ X) =(x) J () a) f(x) =…

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Q: 22 dt at x = 4. ind the linearization of f(x) = 7 - 4 +t

A: Consider the given function fx=7-∫7x+3224+tdt

Q: 19) * (xy)* = e ; f ind y' y' = [1+ In(xy)I y' = -y [1+ In Option 2 O Option 4 y' = [1- In(x None of…

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Q: Consider the function f(x) = ln(x)/x^5. f(x) has a critical number A = __? f"(A) = __? Thus we…

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Q: Let y : R →R be the real-valued function defined on the real line, which is the solution of the…

A: Ans:-  Initial value problem: y'=-xy+x,  y=0=2          solution : y'+xy=x, 40=2          is of…

Q: Find the Tians Farm F(s) = "suy (27>1>0) (1 – s)(1 – e **) 3) f(1) = e',

A: Given problem:- Find laplace transformation of f(t) =et (0<t<2π)

Q: -2+z) ds over t e point (0, 0, 0)

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Q: (c) f(x,u, v) = – log(uv - x" x) on dom f = {(x,u, v) | uv > x² x, u, v > 0}.

A: C.

Q: 4.) Suppose X has moment generating function MX(t) = 0.3e−t + 0.1 + 0.1et + 0.2e2t + 0.3e3t. What is…

A: It is an important part of statistics. It is widely used.

Q: 1. Find the absolute extrema on the given intervälš. a. f(x) = x3 - 6x2 +9x-8; [0,5] b. f(x) = x8/3…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find the largest t-interval such that a unique solution of the following initial value problem is…

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Q: 5. Determine a function v(r, 0, ø) with Av = 0 _in B2 \ B1 satisfying the boundary conditions v(1,0,…

A: Use the cylindrical coordinates to determine the value of r. Now use the boundary conditions to…

Q: [2.73 Find a general Solution of following monhomogeneous limear 1ogeneous linear ODE g+ +1+#)は = e…

A: non-homogeneous differential equations

Q: 16 Q4- Solve the following system of ODE dx dt Eaux"> dy dt = y + 1 =x+1

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Q: Solve the fallowing Cauchy problem U4- Au + cu=0 in R" x(0, 0) On IR"x{t=0}. U = where c is a…

A: Given the Cauchy problem as ut-∆u+cu=0,             in ℝn×0,∞                (1) re-write the…

Q: (a) Express the initial value problem: 1 s'(x) = -f(x), for x +1 f(0) = 1, as an integral equation…

A: The Initial value problem is given as, f'x=-1x+1fx, for  -13≤x≤12                         (1) with…

Q: 1. Show (in terms of e- 6) that a function f : R + R defined by f(1. y. 2) = (2x + 3y + 42) is…

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Q: 1 1 Select all the antiderivatives of f(x)=-+ %3D x² +1

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Q: #3. Solve the following Cauchy problem: 2 Ou + cu = 0 - u = g where c is a constant. in /R" x(0,0)…

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Q: 1. Evaluate these: 1 -x* +c dx *dx (i) x'd< (Ans. x² +c J; (iii) |xdx dx (Ans. ); (ii) (Ans. 2 5 );…

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Q: Determine whether the initial value problem y′ = cos(t + y), y(t_0) = y_0 has a unique solution…

A: Suppose an initial value problem y'=ft,y is provided. If the function ft,y is continuous on a…

Q: Suppose that a population P(t) satisfies dP P F (1-500P), dt 2 where t is measured in days. Ast → ∞,…

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Q: Evaluate: √x(x - 5)dx Solution: √ √x(x - 5) dx = f x²(x - 5) dx by law of exponents/ = f (x² - 5x)…

A: Given problem:- ∫√x(x-5) dx

Q: 1. Evaluate the limits. e' cos (t – 4) dt - 4 (а) lim x2 x2 – 4 e2 + 2 (b) lim x00 e2x + 100

A: Solve the following

Q: 2. Give an example of a regulated function f on [0, 1] such that f(x) > 0 for all æ e (0, 1), So…

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Q: 2. Two ponds are connected and fed by a single stream flowing through them. Pond A holds 500, 000…

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Q: 11. Show that the Beta function, defined by B(x,y) = (1-t"-1 dt , for x> 0, y > 0, satisfies the…

A: the given function is βx,y=∫01tx-11-ty-1dt for x&gt;0,y&gt;0 substitute t=1-s therefore, dt=-ds when…

Q: 2: The necessary condition for existence of the solution of the nonlinear equation x =g (x) in…

A: For any non linear function, to find the existence of its solution between an interval there should…

Q: 1/2 Q2. a) Using Hilbert-Schmidt method, solve y(x) = cos 2x + 2 f,"´ K (x, t)y(t)dt, where Ssin x…

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Q: Find the linearization L(x) ofy = e8# ln(x) at a = 1. L(x) =

A: We will use formula for linearization at one variable.

Q: 4. Use the energy method to prove the uniqueness of the solution for the problem Utt = a²ug + h(x,t)…

A: Given problem is utt=α2uxx+hx,t      0&lt;x&lt;L, t&gt;0ux0,t=t2, uL,t=-t , t&gt;0ux,0=fx=x2-L2 ,…

Q: 2. Given f(x) = x' + ax² + bx has critical numbers at x=1 and x=3, find a and b. .2

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Q: An M.V.U. is unique in the sense that if T, 1 M.V.U. estimators for y (0), then T, = T, almost

A: A sample statistics t is said to be unbiased estimator of population parameterγ(θ) if expected value…

Q: nake/s the DE nonlinear y' =1-xy+ y2

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Q: 7. Use Newtons method with the given X(0) to compute X(2) for each of the following nonlinear…

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Q: 4. (a) Prove that M(x, y) + N(x, y) = 0 can be made exact using an integrating factor that = f(x+y)…

A: To find-  Prove that Mx, y + Nx, ydydx = 0 can be made exact using an integrating factor that…

Q: Chapter 7, Section 7.7, Question 012 Use the inequalities JEM| = ƒ (x) dx 24n2 (b - a) K2 |Er| = f…

A: Given that the integral is ∫0414x+1dx. a) It is required to find the upper bounds on error obtained…

Q: S x2 +2x-10 (2x+4) + 1 JE + 4x +5) Consider dx = x² (x² + 4x + 5) (2x+4) + 1 dx- x² + 4x +5 dx ,…

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Q: 1 4) S(x, y) = Ans. f(0,0) = -1 local max. x+y -1

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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: Let Xi- N co,1) and n=2 auel T= Xi+ Xz Show that Tis a %3D Sufficiency Stabisuic Statistic.

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

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Q: An M.V.U. is unique in the sense that if T, and T, are M.V.U. estimators for y (0), then T, = T,…

A: Answer: For the given data,

Q: 1. Find the optium path for f=xy³ from (2,1,2)

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

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Q: 9. y = Arccot“ Vx 2 Arccot Vx А. Arccot x С. Vx(1+x) x' +x* Arccot x В. Arccot x Vx(1-x) D. - -…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3.Please resubmit the question and…

Q: #3. Solve the fallowing Caucly problem in R" x(0, 0) Uf-Ou t cu =0 on IR"x{t =0}. U = where c is a…

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