Let (Nt)t>0 be a Poisson process with parameter λ=2, Find the following:  (a) E(X3X4)

Q: let w=ln(x2+y), x= 2t, y=4-t. compute dw/dt a) using the Chain rule, draw corresponding tree diagram…

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Q: Chapter 4, Section 4.3, Question 024 Given the functionf (x) = x³ + 3x² – 45x + 8 over the interval…

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Q: (5) Consider the several variable function f(x, y, z) = xe²y + yeš + ze¬². Give a general formula…

A: The given function,   fx,y,z=xe2y+ye3z+ze-x

Q: Let fxy (x, y) = 6 (x – y) , 0 < y < ¤ < 1 and fx (5) = 5 then E (Y|X = }) =

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Q: f(9) = – 10 and | f(t) dt = - 7 then: I· f'(x) dz 0.

A: This question can be solved by using the concept of integration by parts.

Q: Consider the function | dt, defined in [-2, +). Find the local max/min of f(x).

A: Local maxima and minima  Use lebnitz theorem for differentiation

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: The power spectrum of a WSS process {X(t)} is given by S(w) = 1 (1+ o*)* Find its autocorrelation…

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Q: EXAMPLE 2: dz 1 Given that z = x+y,where x = and y 2r. Find by: dt 1 a. Substituting x= and y = 2r'…

A: From the given problem:   z=x2+y2 ; x=1t2 ; y=2t3 a). Now, substitute x=1t2 ; y=2t3 in z=x2+y2 .…

Q: Consider one-parameter members of exponential family of the form, 8(yl0)= exp{d(@)+S(y)+c(0)T(y)},…

A: Given See the handwritten solution

Q: 6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the…

A: Let's evaluate given partial derivative.

Q: Apply the Newton–Raphson algorithm to the function f(x) = x'/3 whose graph is drawn in Fig. 10(a).…

A: Acc. to Newton- Raphson Method  x1 = x0 -f'(x0)f(x0) f(x) = x13 f'(x) = 13x23 Now x0= 1 Hence  x1=…

Q: Let f(x, y, z) = x³e" Vz² + 5 and let x = rt², y = r2t², and z = sin(t) cos(r). (a) Draw a tree…

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Q: T: P2---&gt;P2 defined by T(p(x)) = p(x) + p' (x)

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Q: m(t) = E[e* ]= £e* p(y) +e +e" for y=1,2,3 | - Is this a valid MGF? Valid-TRUE Non Valid -FALSE

A: Given: The mgf of Y is  mt=EetY=∑y etYpy=et2 121+e2t2 122+e3t2 123    for y = 1, 2, 3

Q: f"(x) = 20x3 + 12x2 + 4 with the initial conditions f(0) particular f(x). = 8 and f(1) = 5. Det

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Q: If the 2n RVs A, and B, are uncorrelated with zero mean and E(A²,) = E(B²,) = %3D o, show that the…

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Q: Give a linear stability analysis of the O fixed point in the hollowing ODE[X=8-X² and drow phase…

A: Bifurcation: A qualitative change in the nature of fixed points is called Bifurcation.  The fixed…

Q: 1. If a Gaussian process is wide-sense stationary, it is also strict-sense stationary.

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Q: Suppose X - Bernoulli (0.5) and Y ~ Exponential (2). Suppose further that X and Y are independent.…

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Q: Let (x(t)) be a Poisson process with rate A, and let T₁ = min{t: X(t) > 1} be the first arrival…

A: The first arrival time ( T1) in a Poisson process with rate (λ) is exponentially distributed with…

Q: 4) Consider the function F(x) = f f (t) dt . Find F¹ (7). O F(7)-F(2) O f(x) O f(7) Of(7)-f(2)

A: Given query is to find indicated derivative.

Q: Let A(z) = f(t)dt where f is the function given by the graph bele 3 2 1 2 3 4 5 7 1 -2 -3 -4+ A(5)=…

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Q: Suppose that X ~ fx(x) = 3x²1(0 < x < 1). (a) Verify that fx is a PDF. (b) Derive and sketch the CDF…

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Q: Let f (z) = (z2+1)(z²-4z+3) and I = P.V. f)G-t843) dx. (x² +1)(x²-4x+3) 2-i Given Res f(z)|z=i = and…

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