Suppose that || u|| = 2, || v|| = 1 and u v = 1. Compute || 3u - 2v||2 %3D

Q: 1. Show (in terms of e- 6) that a function f : R* → R defined by f(x, y, 2) = (2x + 3y + 42) is…

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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: Solve the Following Euler's (or Cauchy's) Equations: (1) x'y" – 2x² y" – 2.xy'+ y =0

A: As per our guidelines only first question will be solved.

Q: 4. Suppose is a discrete rv with E(9X + 2) = 20 and E(X²) = 13. (a) Find E (X) (b) Find V (X)

A: a) We will use the formula E(aX+b)=aE(X)+b E(9X+2)=20E(9X)+E(2)=209E(X)+2=209E(X)=18E(X)=2   Answer:…

Q: 1. Prove that for all x, y ER, max (x, y) = x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y}=-

A: What is minimum and maximum Value: For a given set of numbers, the minimum value of the set is the…

Q: Suppose E(X) = 1, V(X) = 2, E(Y)= 3, V(Y) = 4, and E(XY)= 5. (1) Сov (X, Y) (2) Corr(X,Y) (3)…

A: 1) COV(X,Y) =E(XY)-E(X)E(Y)                    = 5-1×3                    = 2

Q: 2 Exercise.8 Find: P4 (x), Pg(x), L P¾(x) P3(x) dx , LIP,(x)|² dx

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Q: Find the values of x,y and z using Gauss Jordan method.

A: We have given a system of equations ,  3x + 4y + z = 102x - 3y + 5z + 9 = 0x + 2y - z = 6 This…

Q: If AB = B for some B # 0, then A is inertible.

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Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

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Q: Let X1,..., X, be independent such that X;|p ~ Bernoulli(p) with pE (0,1), and p~ Uniform(0, 1).…

A: c) Given that X1,X2,.....,Xn be independent such that Xi|p~Bernoulli (p). f(Xi|p)=pxi(1-p)1-xi…

Q: Suppose we have the quadratic function f(x)=A(x^2)+C where the random variables A and C have…

A: A quadratic equation is written as f(x)=Ax2+Bx+C. f(x) has real roots if B2-4AC≥0.

Q: 1. Suppose that Var(X) = 3, Var(Y ) = 4, and Cov(X, Y ) = 1. (a) Find Cov(2X − Y, X + 3Y ). (b) Find…

A: Given, Var(X) = 3, Var(Y ) = 4, and Cov(X, Y ) = 1       To find, a) Find Cov(2X − Y, X + 3Y ).b)…

Q: - If W = xy + y2+1 azw Show that a2w ey %3D дхду дудх

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Q: Consider the linear model Y₁ = B₁ + B₁X₁¡ + ß₂X2i + u; where u; is the error term and where E (u;…

A: 4 main assumptions of Gauss Markov multiple linear model are : Linearity : The errors and…

Q: The number of defects on the front side (X) of a wooden panel and the number of defects  on the rear…

A: Here, fXY (x, y) = c(x+y) Joint Distribution of X and Y can be formulated as: X\Y 1 2 3 Total of…

Q: 3. Solve the following set of simultaneous linear equations using the Jacobi's method.

A: Given,

Q: 1. Show (in terms of e – 6) that a function f : [2, 7] → R be defined by f(x) = Vx² + 1 is uniformly…

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Q: x*y" + xy'+4y= 2x Ina

A: Cauchy linear differential equation

Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

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Q: (d) VX € P(N), XCR. (e) In ɛ N, VX e P(N), |X| < n. (f) Vn e Z, 3X c N, |X| = n. (g) 3me Z, Vn € Z,…

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Q: Solve the following Cauchy-Euler D.E: x²y" – xy' +y = 2x2 + In x %3D

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Q: Let X1,.,Xn be i.i.d with n 2 6, E(Xi) > 1 and Var(Xi) > 0. X1x2 and X3X5 are then. (A) not…

A: Here, X1, X2,........Xn are i.i.d with n≥6 with E(Xi)&gt;1 and Var(Xi)&gt;0.

Q: Draw the Direct Form II implementation of the LTI system of impulse response h[n] = { 1, n even and…

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Q: 2. Suppose the PDF of X is given by fx(x) = 5e-5x(o)(x). Find its CDF.

A: Solution

Q: log, x = 5.3 and log3 y = 2.1, %3D log4 u = 3.2 and log4 v = 1.3. 19. log3 (9xy) 27. log3 (x²y³) 20.…

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Q: 1+ By using the definition In(1+x) = / 1 -dt, show that for a certain range of values of r, t…

A: Solution:

Q: Assuming a Gamma mixture model and using Ez [In p(X, Z)|X, Oʻ]. which of the following is the update…

A: Gamma Distribution:              Basically, Maxiture model is widely used in the…

Q: Show (in terms of e - 6) that a function f : [2,7] R be defined by f(z) = V² +1 is uniformly…

A: In this question, we need to show the given function f(x) is uniformly continuous.…

Q: The Wronskian 1. Show that the functions e", cos x and sin x are linearly independent. 2. Show that…

A: 1. The functions ex, cos x and sin x are linearly independent.2. The functions 1, sin2x and cos2x…

Q: Apply Euler method and Richardson extrapolation for h = 0.2, 0.1 the problem: and abtain g y' = ty…

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Q: 5. 9 ycotx %D CSC

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Q: Suppose, X|0~ Binom(m.0)and e- Beta(a,B), then Var (Y) is equals to, maß

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Q: 4. Suppose that for a particular linear model [2 1 X'X = 1 li 0 1l [14] X'y =| 6 1] 1 8 1) What the…

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Q: the following DE are Bernouli type and solve: 1. y’ – x = y 2. y’ + 5y/x = x 7 y 4

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Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

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

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Q: Verify that u' (t – a) = 8(t – a) by solving the problem x' = 8(t – a); x (0) = 0 to obtain x (1) =…

A: What is Laplace Transformation: Laplace transformation is crucial for control system design. Laplace…

Q: EX: Find the Z. T. of X(X) = cas wok u(k) Soin

A: Z transform of the function

Q: The ACF of the residual u can be used to check the adequacy of the fitted AR(1) model which has the…

A: The given AR(1) model is: yt=2+0.7yt-1+ut The AR model of order 1 is interpreted as the model in…

Q: 1. Prove that for all x, y ER, max (x, y) x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y)=-

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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: Consider the first order linear PDE и, (х, у) + 2и,(х, у) + u(х, у) %3 4х. Find its general solution

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Q: 10 Consider A :3D and y:= Find all re R that minimize || Ar - y|l2.

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Q: Given that X has pmf f(x)=1/(2)^(x+1) , x=0,1,2,... and et<2 , use mgf technique to…

A: Given: X has the pmf as follows, f(x)=1/(2)^(x+1) , x=0,1,2,...et&lt;2

Q: 4. Prove that (À × B) · (B x T) × (T x A) = [ABT)

A: The objective is to prove that

Q: Find the particular member or orthogonal trajectories of x2 + cy? = 1 passing through the point…

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Q: Find the value(s) of k such that A is singular.

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Q: 8. Theorem h° = %3D

A: The figure given below represents the circle. From the angle subtended by the same arc theorem, The…

Q: Theorem 7-13. µ' = E {X (X – 1) ... (X-r+ 1)} = P (). ,where u is the rth factorial moment of X. s=1

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