Consider the stochastic process Y₁ = (1 + y)Bt + (1 + €) (B² – t), where B is a Brownian motion. Show that it is a Martingale.

Q: Multiply -1 2 -3-2 -8 -9 -7 9 00 00 00 00

A: Matrix multiplication

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A:

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A: Solution:-

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A:

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A: Chain rule for total derivative

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Q: (h) Let u(x, t) be given by u(x, t) = a, cos(3nt) cos(2nx). [ an n=1 If u(x, 0) = cos(4x), 0≤x≤/2.…

A: This is a problem of Fourier analysis.

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Q: Z=x+y+ cos(x+y)

A: Given,        z=x+y+cos(x+y)

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Q: Advanced Math b) The curve y= y = x³ + px² - 12x has a stationary point when X=-4 5 i) Show the…

A: Follow the steps.

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A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: The solution is given as

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Q: 1. Evaluate the following iterated triple integrals: pa+ay (a) f f f xy dz dy dx 1 (6) L L L (x² +…

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Q: 4. 2x₁ + X₂ X3 3x₂ + x3 -2x3 2x₁ + x₂ + x3 L = Answer X₁ X4 = 7 x4 = -3 = 2 2x4 = 8 x₂ = M U = x3 =…

A: Given,                  2x1 +x2 - x3 - x4 = 73x2 + x3 - x4 = -3         -2x2  = 22x1 + x2 + x3 -2x4…

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Q: Inverse of a Matrix II. Solve the following 1. Find (1,3) entry of G-¹. 2. Find (3,2) entry of G-¹.…

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Q: Solve the differential equation using inspection method d'y d³y dx5 dx³ = 24.

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Q: Fill in the blanks. Justify your answer. If f has an essential singularity at zo, then for any n EN…

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Q: a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

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A: In the Venn diagram, the set notation is shown as

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A: Variation parameter method

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Q: ) Using each graph of y = f(x), sketch th [(x) and g(x).

A: (a) Given,

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A: Solution:x2+y2-4y=0, y=4-x and axis of revolution y=0above equation x2+y2-4y=0 can be written as…

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Q: Let A be an n x n symmetric matrix, R be an n xm matrix such that with m ≤n), and let B = R¹ AR (an…

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Q: =X C R

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A: Here we have a common point in both of the sets. Also thos two sets are individually connected.

Q: Solve the nonhomogeneous system ty' = 3-2 2 -2 Y + -2t ¹-1

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