18/156) If the Wronskian W of fand g is t'e' and if f(t) = t, find g(t).

Q: • Let X1,...,Xn iid Poisson (0) such that E(X1) = 0. Suppose that Find the level a = 0.05 LRT for…

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Q: Let, f(z) = z-2z +2 (a) Show that, starting from the initial point ro 31 using Newton's method it…

A: Consider the given function.

Q: 3. Find the maximum and minimum values of a 1 āz - on |z| ≤ 1 (where a with la| < 1 is fixed)

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Q: Show that for some number a > 1, we have 1- <= In(a) <= a – 1. Hint: In(a) = S"dx, please check the…

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Q: If the moment-generating function of X is M(t)= e, then the moment-generating 3t function of Y=1+-X…

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Q: If X(t) with X (0) = 0 and µ = 0 is a Wiener process, show that Y(t) = oX %3D is also a Wiener…

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Q: Let X ~ Poisson(λ). Derive the moment generating function of X and use that to find E(X3)

A: Solution: Let X~Poisson(λ) The probability distribution of X is  P(x)=e-λλxx!    x=0,1,2,3,..

Q: H) 9f zyzec then prove thal nl x=4=Z, (alogen) %3D

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Q: n! Prove that L(t") sn+1

A: we have to show that                                                       Ltn=n!sn+1 we know that,…

Q: Let fn E D[0, 1]. Suppose that fh g on [0, 1], and lim fn(1/2) exists. For each x E [0, 1], show…

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Q: If the WSS process {X(t)} is given by X(t) = 10 cos (100t + 0), where 0 is uniformly distributed…

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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: If the WSS process {X(t)} is given by X(t) = 100 cos(10t + 0), where 0 is uniformly distributed over…

A: Find the autocovariance function of X(t)? Is X(t) wide sense stationary? Explain If the WSS process…

Q: Assume x and y are functions of t. Evaluate dx = 9, x = 3, y = 0. for 4xe = 12 - In 729 + 6ln x,…

A: Given query is to find indicated derivative.

Q: Consider the function z=x ln(1+ y“), if x=2-t and y=\t , use an appropriate form dz of the chain…

A: According to the given information, consider the given function z.

Q: 15 Solve the IVP using Laplace transforms. x'(t) = t, x(0) - 4

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Q: 7. A damping system with a negligibly small spring constant is modelled by x' +bx' = a e1 with…

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Q: 9. Building upon Example 5.14, let X be a real-valued compound Poisson proce with Lévy measure v,…

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Q: (a) Let X have the following pdf : S2(x - 1) 1<z<2 S(2) = elsewhere. Compute E(X'), E(2X-1)

A: As per our guidelines we are suppose to answer first question.

Q: Let (B; ) be a Brownian motion with Bo = 0. Define a process (Z,) by Z, = B{l/t for t > 0. What is…

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

Q: (a) Show that the moment generating function of X is given by 1 Мx() - 1<t< 1. 1 – t2

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Q: (a) Consider two MA(2) processes, one with e, = 0: = | and another with 0=-1 and 0; = 3. O Show that…

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

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Q: Let X (t) be a Gaussian process on t€ (0.00) with E(X (t)) = 0 and E(X (t) X (s)) = min (t.s). (a)…

A: Gaussian process In probability theory and statistics, a Gaussian process is a stochastic process (a…

Q: If the auto correlation function of a WSS process is R(T) = k. e-k hts spectral density is given by…

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Q: 43. If f is differentiable and is periodic with period T, show that f' is also periodic with period…

A: First we prove that f'(x) is periodic by definition of derivative. Then we give an example to prove…

Q: find the Laplace transform of VE cos(3Vf). E{VE cos(3V)} =0.

A: We are given that,  Lcos3tπt=e2.25ss..................................................(1) We are…

Q: The moment generating function of X is defined by M(t)=E(etx) صواب İhi

A: True.

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: Let X(t) be a WSS Gaussian random process with ux(t) = : 1 and Rx(7) = 1 + 4 cos(7). Find

A: From the given information, Xt be a WSS Gaussian random process with μXt=1, RXτ=1+4cosτ. Consider,…

Q: 2. Give an example of a regulated function f on [0, 1] such that f(x) > 0 for all æ e (0, 1), So…

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Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

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Q: 68. Show that the asymptotic representation of the Bessel function Jn (kr) for large kr is Jn (kr) =…

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Q: Express the limit lim E (4 cos (272;) + 6)A¤; [2, 4] over as an integral. n- 00 i=1

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Q: Prove that the random process {X(t)} with constant mean is mean-ergodic, T T 1 if | C(t,, t2) dt dt,…

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Q: 11. Prove the absorption law x +xy=x using the other laws in Table 5.

A: To prove: x+xy=x We use the following identities (1) x=x·1 (2) 1+x=1 (3) xy+z=xy+xz    ( This is…

Q: If X ~ gamma(r, 1), show that the moment generating function of is given by if t < A. Mx(t) = { ()",…

A: Given, Mxt=λλ-tr As we know that, Ex=Mx'0Ex2=Mx''0 Now, Mx't=ddtλλ-tr=rλrλ-tr+1

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: Integrate the fuackion f=g regian bonndel by y the en6* y-o ver

A: The function is fx=xyThe region is bounded by y=x, y=6-x, y=0

Q: Let {yk } be the DFT of {x; }, where x = [0, –1, 0, 1] y3 = O i -1 -i 1

A: Here, x0=0, x1=−1, x2=0 and x3=1 We have to find y3 Now, y3 is given by…

Q: 4. Suppose that u(x, t) is defined by a PDE and by initial values (at t = 0): du + to,u= u for all…

A: Suppose that u(x,t) is defined by a PDE and by initial values (at t=0)∂tu+t∂xu=u for all x,and…

Q: 4. If R(T) is the autocorrelation function of a stationary process {X(t)} with no periodic…

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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: Use Laplace transforms to solve the initial value problem x"'+x = cos3t; x(0)= 1, x'(0)=0

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Q: Let x~ possion(alpha). Show that E[x(x-1)(x-2)....(x-k)]=ak+1

A: Solution

Q: Prove that by Gamma Function eit + e' e-st dt 2 s2 + 1

A: We will find out the required result using Gramma function.

Q: Which of the following functions has a maximum y value of 4 Oy= 4cos x y= cos 4x Oy= cos x + 4 Oy=…

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Q: Which of the following graphs is the slope field for dx 12 -3-211. s 2 13 US 111-2-/35 1112 111²-111…

A: Here we have to solve the given differential equation and plot the solution

Q: Prove that by Gamma Function pit +e e-st dt %3D s2 +1

A: Gamma Function: The gamma function, denoted by is denoted by which is convergent for Some…