1/2 Show that ||r|| = + [En]² defines %3D a пorm. j=1

Q: A random process is defined as Y (t) X (t)- X (-a), where X t) is a WSS process and a>0 is a…

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Q: Whch of the futowing tunction is a iner tunctiont Sx)- V3x -4 S(x) = x +5 O oton O outen f(x) = 2x…

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Q: (a) Suppose X U (0,n), where n is a positive integer X-[X] U (0, 1). (b) Use the result of (a) to…

A: De Moivre's theorem gives an axiom for computing the powers of complex numbers. We first gain some…

Q: The causal sequence {x} Xg = (G)* (k> 0) %3D XK Determine the z transform

A: given                                                xk=12k; (k≥0) we have to find z-transformation.…

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: What is the general solution of the given higher order DE xy" + x(y')² – y' = 0 ? Select the correct…

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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: x + 174 Evaluate dx, by expressing (x – 8)(x + 9) the integrand as the sum of the partial fractions.

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Q: 2. Suppose that X is normally distributed with u =-7 and o2 P(X 2x) = 0.84. 14. Find the value of x…

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Q: z2-1 What is residue of f (z) = at z=3 ? %3D None -8 Res (f(z),3) = 3 %3D 8. Res (f(z),3) = %3D 8.…

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Q: 2. Expand the function f(x) = tan-1 x up to the first two non-zero terms in the Taylor's polyno-…

A: Solution is given below:

Q: x,x→X,x mysa rft bns astemee a.s. X→X=Xn→X

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Q: 2. Estimate the largest value of x that allows e* to be approximated to 0.01% accuracy by the…

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Q: 13 Approximate |x- 12 dx, by computing Lf (P) and Uf (P) for the partition P = {11, 11.5, 12, 12.5,…

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Q: K=Zp(t) ,then f(x)=x^p-t is irreducible over K[x]

A: GIVEN: K = Zp(t)

Q: Suppose (i) (ii) X, has a pdf f(x) = ₁ ²e²³/12 16 0 [x₂²e¯³3²/2² 4 0 X₂ has a pdf f₂(x₂) = ₁ (iii)…

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Q: (b) Integrate the function f 1 dx by using substitution and partial fraction. x(2x -1) Hence, show…

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Q: The bivariate beta type I pdf is fx,„x, (x1, x2) = Kx-x" (1 – x1 – x2)e-!, x1 > 0, x2 > 0 and x1 +…

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Q: Part (b) 7s +4 Find L-{F(s)} (s + 4)° Let F (s) = s2 + 4

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Q: The total public debt D (in trillions of dollars) in the United States at the beginning of each year…

A: Given : t D 0 5.6 1 5.842 2 6.148 3 6.518 4 6.952 5 7.45 6 8.012 7 8.368 8…

Q: Q3: Find the Wronskian for the following solutions. Y, = 1, Y =In

A: Wronskian= 112ln1+x1-xd1dxddx12ln1+x1-x= 112ln1+x1-x01x+11-x=1x+11-x

Q: x2 dx by computing Lf (P) and Uf (P) for the partition P = -12, -6, 0, 6 Approximate -12 Lf (P) Uf…

A: Consider the given information

Q: Q4 Fined a Sp litting field of xt_2.( show your work) (a) aver Q

A: a) Over ℚ The degree of fx=x4-2 is 4, so the splitting field K of f(x) must contain its 4 roots.…

Q: Find the weighted integration norm (f, f) = | f(x)f(x)w(x)dx of the given polynomial on C[0, 1].…

A: Norm of a vector is defined as f=f,f.

Q: 2 Let xk = E(k+1)(k+2) for all k e N and define S, = Ek=1 ®k• (a) Evaluate Sn as a function of n.

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Q: An insurance company offers its policyholders a number of different premium payment options. For a…

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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: which of the following property is correct for J (x) d dx n-1 .a d (x" Jn (x))=x" Jn+1(x) dx .b d…

A: For Bessel function ddxxnJnx=xnJn-1x

Q: 1.9.21. Let X be a random variable of the continuous type with pdf f(x), which is positive provided…

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Q: Exercise 2: Let 0, and 02 be two independent unbiased estimators of 0 such that Var(01) = o? and…

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Q: _5. SEdx = In\x| + C and Sdx = In]x²| + C. _6. Sx" = _7. If G(x) is an antiderivative of g(x) and…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: 13 Approximate x² dx by computing Lf (P) and Uf (P) for the partition P = {-26, –13, 0, 13. -26 LF…

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Q: Let X and Y have the joint p. d. f . sx+y if 0<x, y < 1 elsewher f (x, y) = %3D The covariance…

A: Given X and Y have the joint p.d.f. fx,y=x+y  if  0&lt;x,y&lt;1    0          elsewhere

Q: (11) Let G(x) = 1 In(1+t²)dt. (a) Find G(1).

A: Solution Given G(x)=∫1xπ ln(1+t2)dt.We need to find the G(1)

Q: d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4…

A: Topic:- application of integration

Q: Q4 Consider the PDF 6x(1 – x) 0 < x < 1 Px (x) = otherwise Find P(0.5 < X < 0.7) and E(X).

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Q: Find the PSD of a random process x(t) if E[x(t)] = 1 and Ryx(t) = 1 + e-alt|

A: Answer: For the given data,

Q: -B/ls//E-x] in (6.14) is distributed as at =

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Q: 1. Let X have the moment-generating function Mx (t) = (1– 2t)-r/2 , t< ½ (a) Find Var (-5X) +…

A: Given  X~χ(r)

Q: 2. Let X denote the amount of space occupied by an article placed in a 1 – fr packing container. The…

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Q: Rxx(t,t + t) = sin (6t + t)e-t

A: Define autocorrelation function: Let there be a time series y1,y2,...yn The autocorrelation function…

Q: The numerical integral formulation of I = Sº f(x) dx using composite Simpson's 1/3rd rule is a. h/3…

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Q: Calculate the residue of ez.z-5 at z=0

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Q: Let X denote the temperature at which a certain chemical reaction takes place. Suppose that  X has…

A: Given : Pdf of X : f(x) =194-x2     -1≤x≤20                       0.w

Q: 17. Find the values of p for which the integral 3-2, dx converges. 3-2p Орe(-1,1) Op > 1 Op 1 Ops1

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Q: 4 Q2: Let J 2+5x-14 find the integral of the function by Partial Fraction ?

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Q: J arctan x dx A C In(x2) + C In(x² + 1) + C x arctanx x arctan X - | 1. x arctan x +- In(x2) + C x…

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Q: 3. Prove that if the more general form of the Cobb-Douglas production function Y = AK" L %3D…

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Q: A random process is defined as Y (t) = X (t) - X (i- u), where X (t) is a WSS process and a >0 is a…

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Q: Find the PSD of a random process X(t) if E[X(t)] = 1 and R(T) = 1 + e-1T| x,

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.