Q. Two: For a random process X(t) with E(x2(t)) = sin(t) we have Pxx = %3D %3D A) 0 B) 1 С) 2 D) 3 E) None

Q: (c) Infer E[W] without resorting to lengthy calculations but make sure you justify your inference.…

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Q: 2- Suppose = {xt)dt . Find ES and d acconding the statistical characteristics of xt).

A: For a continuous random variable X, a probability density function is a function such that (1) f(x)…

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Q: (ii) For what value of 0, the random variables Y, and Y, are uncorrelated.

A:

Q: Let A, BC X. Is Bd(A) C Bd(B)?

A: We want to check for A, B ⊂ X Is Bd(A) ⊂ Bd(B) true or false.

Q: 4 + u*du then

A: Here we find the derivative of given integral

Q: Find the covariance of Y,, Y, and Cy.y.

A:

Q: Prove that if 'X' and ʼY' are 'random variables taking real values then [E(XY)}]SE[X°] • E[Y²].

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Q: 1 1 Find E [X (1)] and 2 random variable with P (Y = 0 ) = and P (Y = T/2) Rxy (0, 1).

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Q: Q4 Sampling at the argument values t,= 1, t= 2, ty= 3 and ty= 4 and the discrete function is fita) =…

A: Given: The argument values, t0=1, t1=2, t2=3 and t3=4 and their corresponding discrete functional…

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Q: Suppose that X~X(v) and Y~X"(n). If μx = 6,0 y a) State with parameter(s) the distribution of W. b)…

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Q: dy 11. If x? + xy – 3y = 3, then at the point (2, 1),- dx (A) 5 (B) 4 (C) (D) 2

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Q: Task 16. Let To be the time it takes a standard Brownian motion to hit a. Find the probabilities 1)…

A: Given information in question:-Since is time it takes a standard Brownian motion to hit .The…

Q: 4. Suppose the moment generating function (mgf) of any random vector (X, Y), is given by M(t1, t2),…

A: False

Q: Q1: Find 1) e (3 + e6t)2 2) l {e-3t (t + 1)²}

A:

Q: 4. Suppose random variables X; ~ N(Hi, o?), for i = 1,...,n, and X1,..., Xn are mutually…

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Q: Q 6.2. Let X = (X1, X2, X3)T MVN(x, Ex) where 2 -3 -() 1 fx = and Ex: = 6 -2 L - -2 - (a) Compute…

A: Given,  where  and

Q: 4

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Q: 1-) let fCE) be a differentiasle funckion. Show that pCe) dwce) = cA)wC6) - ecalwca) 3) Solue the…

A: We will use the basic knowledge of integral and differential calculus to answer these questions…

Q: 7 dt, where x> 2 Find dx for y = J 31+7 3

A: We shall use the Newton Leibniz formula

Q: n =10; 2 x, = 67;2 x = 493; 2y; = 85; 2 x,y; =603 , find_ (x; – x)´ = ? Also, please i=1 find…

A: Given information: n=10 ∑Xi=67∑Xi2=493∑Yi=85∑XiYi=603

Q: 2.2.3 Example C The inhomogeneous equation Yk+1 – kyk = 1 (2.21) | has pk = k and qk = 1. Since k…

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Q: 2(1-z) Evaluate S-" ==-2) dy dx dz

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: Q 6.2. Let X = (X₁, X2, X3)¹ ~ MVN (ux, Ex) where -3 7²) μχ = Compute the distribution of Y and Ex =…

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Q: (i) Find the covariance of Y1 and Y2, Cy, Y,

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Q: ) Find MThe equation of The normal to 5 at the point (a, 4) y=dx

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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…

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A: The correct option is, (A) Only I  The detailed description is as follows below:

Q: -20x-2) SS f(x.y) dy dx + f(x.y) dy dx= f(x.y) dx dy, then g(6a)+h(a)= if (4)6 0

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Q: -3 Let A = -4 -3 -1 9 Define the Lnead teanofamatia T:IR²> IR° by T2)= AR. Find the inages of ů= [oI…

A: Put the value of u and v in the definition of T

Q: Let W(t) be Brownian motion. Using Ito's lemma evaluate | (4w (t) – 124W (t))dW(t)

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

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Q: Find et 1+ e2t 0(t + 1) dt.

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

Q: Check the equation for calculating the sums of squares in a DCA, prove that:

A: Given information: The equations for calculating the sums of squares are given.