Suppose that Yt follows the stationary AR (1) model Yt=2.5+0.7Yt−1+ϵt, where ϵt is i.i.d. with E(ϵt)=0 and Var(ϵt)=9. Suppose that YT=102.3. Compute  Yt+1|t=E(Yt+1|Yt, Yt-1...).

Q: 7. Evaluate Soy4 2 - y dy using Gamma/Beta function.

A: The solution is given as

Q: d Evaluate the following derivative: dx (1 + t² dt. Oxv1 +x4 + v1+x² Main Content None of these O…

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Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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Q: Let r(æ) = f(g(h(x))), where h(1) = 3, g(3) = 2, h'(1) = 9, g/ (3) = –2, and f'(2) = 5. Find " (1).…

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Q: Consider the function with function equation y = (2x + 6) e*. This function has a unique critical…

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Q: If X is an unbiased measurement of a true value Pg, and U(X) is a nonlinear function of X, then in…

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Q: Let f(x) = cos t dt ,x> 0. Then Ax) has (a) maxima when n = - 2, - 4,- 6, . . . . (b) minima when n…

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Q: Estimate g(1.2) − g(1) if g'(1) = 4.

A: Given: g'(1)=4 Now, Using the Linear approximation formula:

Q: dx Suppose 10 = x + y' and both y = f(x) and x = g(t). If = 2 when x = 1 and y = 3, %3D dy when x =1…

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Q: 7. If g(4) = 3k +7, g(9) = 7, g' is continuous and %3D J g'(x)dx = 2k? + 13, find the value of k.

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Q: Exercise 1.3.8: Find an implicit solution for dy dx = x² + 1 -, for y(0) = 1. y² + 1'

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Q: b. foet t'dt

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Q: dy x3 + 2xy. y 7. Find for the implicitly defined function dx

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Q: 2. Estimate g(1.2) – g(1) if g'(1) = 4. -

A: Given, g'(1)=4. The formula for the linear approximation is, g(x)=g(a)-g'(a)(x-a), where x is near…

Q: Given G(x, y) = 6y²(e(²) +e (¹)), where and y are found to be In 3 and 3 with maximum possible…

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Q: Page 6 of 7 7. [4] The total accumulated costs C(t) and revenues R(t) (in thousands of dollars),…

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Q: a function y = f(x) be implicitly given by the equation y²-x²y³ - cos (πy) = xª. The point (-1,1).

A: Topic:- application of derivatives

Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

Q: ) Find y as a function of a if z?y" + 2xy' – 20y = 0, %3D y(1) = -6, y'(1) = 1. %3D y =

A: Differential equation

Q: [(²5+4) dr. -3 (c) Determine dr, where x > 3.

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Q: Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY

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Q: Suppose {Y} is a stationary process and we observe the values Y₁ = 6, Y₂ = 5, Y3 = 4, Y₁ = 6, Y5 4.…

A: answer is explained in explanation sectionExplanation:

Q: b) f(x) = v3+ x² at x = -1

A: