If Z; is i.i.d N(0,y²) and X1~ N(0,o²) be independent of all Z's. Let Xi+1 = pX;+Z; for all i = 1,2, ... %3D y? then Xị is stationary 1-p2 Show that if o² =

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Q: In the figure, ZY = ZX and YZ is produced to T. Prove that YT> XT. Y

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Q: 3. Recall that x - Poisson(0) = Mz(t) = e"(e*-1). %3D A. Derive the MGF of Z = (F - 0)/ /0/n where F…

A: Please find the solution below. Thank you.

Q: A large but sparsely populated county has two small hospitals, one at the south end of the county…

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A: Given information: It is given that Bt is a Brownian motion with B0 = 0.

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Q: Q1) Suppose w = x = cos? t, y = sin? t, z = dw Evaluate at t = 3, by using the Chain Rule dt

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Q: 1 prove that | e -ym dy = mr(m) -ут

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Q: The residual of ŷ; is defined by e, = y, – ĝ.. (1) Prove Σ -0 and Σiι u ΣΗ. (2) Prove E1 T;ei = 0…

A: (1) In problem 1 we have to prove that : a) The sum of residuals in regression model that contain an…

Q: Let SINGLEDFA = { | M is a DFA and for all s e L(M),|s| = 1}. Show that SINGLEDFA is decidable.

A: Detailed explanation mentioned below.

Q: Let T : (0 → l defined by T(Xn)) = ( n. (a) Prove that TE B(l, l∞) and ||T|| = 1.

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

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Q: Let the functionsf and- be continuous in some rectangle a <t < B. y < y < dcontaining the point (to,…

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A: Given, ur,θ=0 satisfies ∇2u=0 in r&lt;1. Also u(1,θ)=fθ To show ur,θ=1-r22π∫-ππfϕ1-2rcos(θ-ϕ)+r2dϕ…

Q: Consider h(x,y, z) = cos (xy) + eY² + In (xz) at the point P ( 1,0, = 1 Deter-

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Q: Find for x = x(t) defined implicitly by 25+25 x In(t) = e25xt Also evaluate dt at (t, x) = (1,1).

A: Given,25 + 25xlnt = e25xtTaking 'log' with base 'e' on both side, we getln25 + 25xlnt = lne25xtln25…

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Q: 2- The work can be computed as: W= fp dV. Using a combination of the trapezoidal rule, Simpson's 1/3…

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Q: X+ xy B. Evaluafe the tripe in tagral S5* xy dydzdx,

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Q: 3) Suppose the joint pdf of lifetimes of a certain part and spare is given by f(x,y) = {° e-*+), 0…

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Q: If z =e* + In(xy) Evaluate- ,and ,at the point (1, 2). Hence, calculate the change in z when x…

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Q: Find e² in the form of u + jv and le²| for z = 2 + 3nj

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Q: S 1.Prove that L (coswt) = %3D s2+w2

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Q: If the moment-generating function of X is a. M(t)=(1–21)"", 1 < ½, Find the p.d.f of X hence use it…

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Q: Generate the points on the Elliptic curve E: Y? = x + 23 over Z7. Compute 25 and 3S, where S is (6,…

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Q: Consider the S.mpto lincar rogressic 3:0n m adol Y tX; t U ukon exp(az.) You have the fallow. ng…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: If z = e4x + y In(x), find zx and zy. Zx Zy %3D

A: 1) The given function is: z=e4x+ ln(x)

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Q: t DR) dende Dartine dövßes e te than show that Deo) X DR1) to DG20). o is atoxphic

A: To show D20×D21 is isomorphic to D420: Define a map f:D20×D21→D420 by fa,b=a×b a×b∈D420: Suppose a…

Q: Compute the flux

A: by divergence theorem flux=∫∫sF.ds   =∫∫∫E div F dv Given F=x,y,zand   S; is the boundary of the…

Q: Let {x; t = 1,2, ...} be a covariance stationary process and define y, = Cov(x, x+h) for h = 0.…

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Q: Find the value of Res(f'(2), 20) if zo is an isolated singularity off.

A: Let us start finding the value of  Res(f'(z),z0)   z0 is an isolated singularity of f

Q: If A = ze?xVi VxA at the point (2,0,3) is + 2xycosy j+ (x + 2y) k then the valueof

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Q: Y Z H K Given: YX = HX, mZY=mZH, MZZXY=mZKXH Prove: YZ = HK er: AZXY = A by reason

A: Using , Angle - side - angle test,

Q: 15.If the Wronskian of f and g is t cos t − sin t, and if u = f + 3g, v = f − g, find the Wronskian…

A: Consider the provided information, Wf,g=fg'-gf'⇒tcost-sint ...... (1) Find the Wronskian of u and v.…

Q: Let X and X, independence r.v. have same moment generating function (-) where tsa, let Y=aX+bX, ,…

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Q: Suppose w = In(æ² + y² + z²) , Compute dw/du and dw/dv in two different ways: ue3" sin(9v) , y :…

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Q: 1) Let s,T: e defined by Sx = (0,x1, X2, - ) Tx - (x2,X3, Xyy ..) .. Show that (i) Ilsil = TII = 1.…

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Q: 1- Find dwi dt at the given value for w ==+2,x = cos (1), y = sin (1),z = w =-+ at = 3

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Q: The values of m and k that makes the ODE (yx+ )d ym = x*(ny)-In(x*) dy %3D homogeneous are m=-3, k=4…

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Q: 1.) Given: T and R trisect SW XS = XW ZS = ZW Prove: XT = XR S T

A: Given that: T and R trisect SW.XS=XW∠S=∠W

Q: (c) The region between the loops of the limaçon r = 1 + cos 0.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.