The joint pdf of two random variables X and Y is(ke - (k-1)y for 0

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Answered: The joint pdf of two random variables X…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let f(x, y) = In(x²y³), where a = s2 + t² and y = 2s + 3t. %3D Which of the following is a correct representation for ? as O af (군E) (20)+ (2) 2s + 3t %3D ds s2+ t2 fe 2 3 Gi) (2t) + (3) 2s + 3t %3D ds s2 + t2 fe 2 3 ds s2 + t2 2s + 3t o af (2) 3 (2s + 2t) + (5) 2s + 3t as s2 +
Question 7
Z1 is a Gaussian zero mean random vector of size |Z2 Suppose that Z 1 1 2 with Covariance matrix [K Given Z1 = 2, what is the MMSE estimate of Z2?
Let S be a linear transformation from R³ to R² with associated matrix 2 2 4= [3 2 3] A Let T be a linear transformation from R² to R² with associated matrix [11 02 2 Determine the matrix C of the composition To S. C = E B -
ACTIVITY 2.22. Let C = {x, y, z}, D = {a, B}. List all elements of: %3D (a) C x D, (b) D x C, (c) C x C, (d) D x D. (e) Make a conjecture regarding the number of elements in a Cartesian prod- uct. Then come up with a convincing argument in favor of that conjecture.
2.8 Consider the triangular random variable with pdf 0 f(x) = X X 2a (b − a)² (2b − x) (b − a)² if x 2b, if 2a < x
Exercise 6. Suppose X1 and X2 are independent standard normal random variables. For a constant a let Wi = cos(a)X1 – sin(a)X2 W2 = sin(a)X1 + cos(a)X2 |3D Show that W1 and W2 are independent standard normal random variables. Remark Geometrically the given transformation is just a rotation of the plane by an angle a. So the conclusion is simply a reflection of the fact that the joint distribution has circular symmetry; i.e. is invariant under rotations.
Four cards are labeled with the numbers 1, 2, 3, 4, and then two of them are drawn. (Their orderwill not matter.) Let S be the sum of the values of the two cards drawn.(5 points) Find the range and probability mass function of S.(5 points) Find the expected value of S.(5 points) Find the z-transform of S.
2. trace. Let n = 4 (we choose 4 for calculation simplicity, but the following are true for arbitrary n). Consider the following linear transformation: tr : R" +R a11 a12 a13 ain ... a22 a23 a2n ... a21 a32 a33 Ha11 + a22 + a33 + ...+ ann = ... a31 i=1 An3 ann ... anl an2 Let In be the n x n identity matrix (or equivalently, a vector in R""). Calculate (A) that tr(In) = n. Let A, B be two n x n matrices (or equivalently, a vector in Rn*). Calculate that (B) tr(AB) = tr(BA). Hint. Write A = [aj] and B = [br1]. Write down the diagonal of AB and BA in terms of aij and bri. Then compute tr(AB) and tr(BA).
Use the age transition matrix L and age distribution vector x₁ to find the age distribution vectors x₂ and x3. L = 7 ↓ 1 0 2 20 00 -8 ↓ 1 Need Help? 00 0 → 0 Then find a stable age distribution vector. -0- x = t 1 X1 = Read It 100 100 100 100
22 Let X and Y be jointly Gaussian random variables where oy= oy and p =-1. Find a transformation matrix such that new random variables Y, and Y, are statistically independent.

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The joint pdf of two random variables X and Y is (ke z (k-1)y for 0