Prove that the process defined below is a martingale

Q: Expand f (x) = v(1 - cos x), 0 < x < 2n in a Fourier series. Hence evaluate %3D | 1 1 1 1.3 3.5 5.7

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Q: Compute cond(A)∞.

A: Given:  A=1010109  , b=10099 To find: condition number of matrix A under ∞ norm.

Q: 808 Find the initial value of the transfer function X(s) : s(s²+2s+101) 4 1 8

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Q: iv. Heteroscedasticity occurs when the disturbance term in a regression model is correlated with one…

A: as mentioned the answers of iv), v), vi) are as follows,

Q: 3) Compute the inverse Laplace Transform. e-3s Y(s)= s²+2s+2

A: (.). Given function is ,           If   , then

Q: y" + 4y = 4t² – 4t + 10; y(0) = 0, y'(0) = 3 %3D %3D

A: Note: As per bartleby rules only one question have to be done. So please upload other seperately.…

Q: Consider the following configuration of solar photovoltaic arrays consisting of crystalline silicon…

A: From the given circuit we can observe that there are two subsystems connected in parallel. Each…

Q: This is a Macroeconometrics question: 2. It has been shown that given the process yt = a +3t+Et, Yt…

A: The given process:  is not a stationary process.The first difference of  is It must be shown that…

Q: Find the fourier series expansion of f(t)

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Q: Consider the ARMA(2,1) process (1+0.6L)(1+0.2L)y, = (1+0.5L)e, . (a) Construct an autocorrelation…

A: To determine:  ACF of ARMA(2,1) process Given: (1+0.6L)(1+0.2L) yt= (1+0.5L)et

Q: (a) Consider two MA(2) processes, one with e, = 0: = | and another with 0=-1 and 0; = 3. O Show that…

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Q: H Is the Linear cartrol process, ச + 0 A B AB = ( 11 ) ( ) = ( ) 6 locally null cartrollable?

A: To determine if the linear control process is locally completely controllable, we need to check if…

Q: Given the LTI model for the behavior of the channel as y(n) = y(n – 1) + 2x(n) and the input…

A: Given LTI model for the behavior of the channel as y(n)=34y(n-1)+214x(n) and the input sequence…

Q: Solve the ODE: xy"+2y'-xy Oby using the Frobenius method.

A: Given that ODE: xy''+2y'-xy=0                    .....1 We know that the solution to this ODE is:…

Q: If E(X") = (r + 1)! 2", then, the moment generating function Mx(t ) = E(eXt) is (1-2t)2 False True O

A: If we Calculate first moment by using both the expression. It should be same otherwise it is false.

Q: Use the Laplace transform to solve the given initial value problem. For technical reasons, write uç…

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Q: Consider the growth of a population p(t). It starts out with p(0)=A. Suppose the growth is…

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Q: у +9y -t Floe, угодно, у' (одно

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Q: hat are the partial fraction decomposition and the inverse Laplace transform of the given function

A: Given: Fs=1s+1s2-1

Q: hT指 Find all inflection points of the function S(x): S6)= In (x²-Zx+5)

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Q: PROCESS A: "Driftless" geometric Brownian motion (GBM). familiar process: dS = o S dW with S(0) = 1.…

A: From the given information, for process A dS=σSdW with S(0)=1

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: Find the generating functions of p[x sj), p[x j+ 1], and p[x = 2j] in terms of p(t)

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Q: 4.0 f(t) = 3 – e-3t + 5 sin 2t

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Q: A stationary random process X(1) has autocorrelation function Rxx (T) =10+5cos(27) +10e -2171. Find…

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Q: Let X(t) be a Gaussian process with px (t) = t, and Rxx(t₁, t₂) = 1+2t₁t2. Find F X(2) < 33

A: From the given information,  X(t) be a Gaussian process with μXt=t and RXXt1,t2=1+2t1t2. Consider,…

Q: 2t If X has moment generating function M (t) = the E (X) is equal to 1+3t

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Q: Consider a semi-infinite elastic string that extends along the x-axis from x = 0 to infinity and let…

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Q: apply the transformation Utt = Uxx V(x) = U(x) + 8t 0<x<L U (0) = 5t v (²₂x) = 43

A: To solve the given partial differential equation (PDE) and apply the boundary conditions, we'll use…

Q: Use the Laplace transform to solve the given initial-value problem. у" + у %3D 6(t — 4п), у(0) 3 0,…

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Q: c) Find f(-1) if f(0) = 2, f(1) = 9, f(2) = 28, f(3) = 65, f(4) = 126, f(5) = 217. %3D

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Q: 6. { C/G +4y= sint, 0, 0≤t<2m, t≥ 2, y(0) -3, (0)=1

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Q: In Exercise 15, you found the second solution to the Legendre equation for n=0 and n = 1: Qo(x) =…

A: What is Legendre Function: Legendre equation of order n refers to a second order differential…

Q: PROPOSITION 8.2 Suppose F has continuous first-order partial derivatives, and N (F. x,x) is the…

A: Given information:The function has continuous first-order partial derivatives. is the image under an…

Q: Use the Laplace transform to solve the given initial value problem. y(t) = 0 1 2 exp(1 t) + 1 1 -…

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Q: Approximate the solution of the Laplacian equation over the isosceles right triangle to compute…

A: Concept Used The Gauss–Seidel method is an iterative technique for solving a square system of n…