Consider AR(1) process r = (e₁, te Z.) is white noise such that 21, with initial condition ro~ N(0,4), where N(0, 1). Assume that Cov(ro. )=0 for all t. + ~.

Q: Consider any(n) + an-1y(n-1) + + a1y' + aoy = f(x) where an, ...a1, ao E R, where an 7 0. ... (a)…

A: consider anyn+an-1yn-1+.....+a1y'+a0y=fx            ...i where an, ......., a1 , a0∈ℝ where an≠0 (a)…

Q: Let fxy (x, y) = 6 (x – y) , 0 < y < x < 1. If E (X) = , E (Y) = Cov (X, Y) = then %3D

A: Given,fXY(x,y)=6(x-y) ; 0&lt;y&lt;x&lt;1E(X)=34E(Y)=14

Q: Q 6.2. Let X = (X₁, X2, X3)T~ MVN(ux, Ex) where -3 (1) μχ = Compute the distribution of Y and Σχ -…

A: Let  where

Q: 5. Suppose z = f (x, y), where x= g(s,t)and y= h(s,t). Show that ôz d²x ¸ ôz ô²y %3D ô°z ôx ôy ôz(…

A: Chain rule of partial derivatives: Let us consider a two variable function  z=f(x,y)  where ,…

Q: Q14) (A) (t) sin(2t) e-st dt = (B)e- e- (C) se-F. s2+4 (D) 2e-8. 82 +4 (E) e

A: The integralFrom the shifting property, we haveHere

Q: (d) Are X and Y independent? Justify your answer.

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Q: Let n I be a positive integer. Show that the functional •1 S[y] = √² dx (y')"e", y(0) = 1, y(1) = A…

A: Given that, n&gt;1 be a positive integer.

Q: What is the domain of r(t) = e'i + j+ (t + 1)~³k?

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Q: A. T(f(t)) = |B. T(ƒ(t)) = f(−t) from Pg to Pg = tª ƒ' (t) from P₂ to P5 = f(t)ƒ' (t) from P7 to P13…

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Q: Show that the operators Ix=x 0x = 0 Tx (t)=n't & are Linear. 6

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Q: If F (x)= [V5t² – 3t dt find F'(3). a) 0 b) Viz c) d) 3 e)

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Q: Let w = x +y+ z, x = u³ + v³, y = eu, z = u – v and u = t+1, v = e*. Find the value of w (0). %3D…

A: Given: To find: The value of w'(0).

Q: Evaluate: O 3 0 S''(√ri+ - i + ln(2) j+ 4 1P ( 1 , 2 + (1+1) 1] (-1) ² e 3 0 2 + + m (2) 1 + (1 - 1)…

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Q: i) Assume a MA(1)-process given by Y = c+ e +6ɛ,-1, E, ~ N(0, o?), t= 1,... ,T. Compute the…

A: A time series is a sequence of observations taken sequentially in time.

Q: A non-linear function is given by f(2) = a*-1 Where a is a constant. b) Define the perturbation…

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Q: p = m(1-dt) for d (buisness)

A: In this question , we can solve for 'd'.

Q: f(2) 1 dt, then f'(z) = ++1

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Q: if x² + y² =t -- and x* + y* = t dy prove dx 1

A: Given, if  x2+y2=t-1t and  x4+y4=t2+1t2 To prove that  dydx=1x3y

Q: 5) Determine the entire function f(2) = u+ jv satisfying Re(f(2)) = u(x, y) = ae" cos(y) + r? – y²,…

A: That's easy. Thumb up. Have a good day!!! We use Milne Thomsan's theorem

Q: Q1)A nisy transmission channel has a per digit error probability Pe=001 Calculate the propability of…

A: Note: As per guidelines ,we are supposed to solve only one question at a time. please repost the…

Q: 5. Find F'(z): 5 12 1 (a) F(z)= dt e+1 2x

A: we have to derivative with respect to x

Q: Prove that if n> m - 1, then J,(x) = 2(x/2)"-m

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Q: Ut for 0 <x <l u(x,0) = x u(0, t) = (1, t) = 0

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Q: Are these equation separable 1.s2+ds/dt = (s+1)/st 2.dr= b(cosx dr+ rsinxdx) 3.y'=ye(x+y)/(x2+2)

A: The objective of the problem is to determine whether the given equations are separable. A…

Q: 2(x-1) If y = Vx² – 2x then y' 3x2-2x

A: For the first part, we differentiate the given function y with respect to 'x' and use change rule of…

Q: 7. Which of the following is the potential function for F = (2ху + 1,х2 + 2yz, y? — 2)? а. Ф(х, у,…

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Q: Q.3 a) If acceleration components of an electron are given by d²x - b d²y 0, dt dy dx b- = a dt dt?…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: y let f(v₁v₁w) = (eº, cos(utv) tsin (utv+W)) and g(x, y) = (e², (os (y-x), ey). Calculate fog and…

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Q: Find o r(t)dt if r(t) = (cos t, sin t, 3t²). %3D O A.O B. (0, 2, ³) OC (0,0, x³) O D. (0, 2, 7) O E.…

A: We have to choose the correct answer from the given option

Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: If ƒ is continuous and f(t) dt = 16, find the integral

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Q: Q3/ choose the correct answer: 1-for the r.v.x having pdf f(x), then the moment generating function…

A: 1.) C ( None of them ) according to the definition.  2.) The value of V( 2c + 4x ) = 42 V(x) = 16…

Q: (a) Assume Y₁, Y2,..., Ye are independent Poisson(₁). Let n= Ei Yi. Show Y = (Y₁, Y2,...,Y)'n~…

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Q: If L{f (1)}= e-(s+1)f 12sin?t dt_then what is f (f)?

A: