Cauchy schwartz - Study guides, Class notes & Summaries

UNIVERSITY OF CALIFORNIA, SAN DIEGO Electrical & Computer Engineering Department ECE 250 - Winter Quarter 2019 Random Processes Solutions to P.S. #5 1. Cauchy–Schwartz inequality. (a) Prove the following inequality: (E(XY ))2 ≤ E(X2 )E(Y 2 ). (Hint: Use the fact that for any real t, E((X + tY ) 2 ) ≥ 0.) (b) Prove that equality holds if and only if X = cY for some constant c. Find c in terms of the second moments of X and Y . (c) Use the Cauchy–Schwartz inequality to show ...

What is the formula for computing the distance between these two points: (x1,y1), (x2,y2)? - √( (x1-x2)² + (y1-y2)² ) What is the formula of the length of vector X = [x,y,z]: denoted by |X|? - |X| = √( x² + y² + z² ) What is the formula for dot product of the following vectors: X = [x1, ..., xn] and Y = [y1, ..., yn]? (Definition 6.1) Dot product symbol we'll use: . - X.Y = x1*y1 + ... + xn*yn What is the formula for the law of cosines? - |X-Y|² = |X|² + |Y|² - 2|X||...

TestBank for Introduction to Econometrics 3e Stock Watson SM For Instructors Solutions to End-of-Chapter Exercises©2011 Pearson Education, Inc. Publishing as Addison Wesley Chapter 2 Review of Probability 2.1. (a) Probability distribution function for Y Outcome (number of heads) Y  0 Y  1 Y  2 Probability 0.25 0.50 0.25 (b) Cumulative probability distribution function for Y Outcome (number of heads) Y  0 0  Y  1 1  Y  2 Y  2 Probability 0 0.25 0.75 1.0 (c) ...

Homework 0 solutions CS229T/STATS231 1. Linear algebra (0 points) a (dual norm of L1 norm) The L1 norm k · k1 of a vector v 2 Rn is defined as kvk1 = nX i =1 jvij: (1) The dual norm k · k∗ of a norm k · k is defined as kvk∗ = sup kwk≤1 (v · w): (2) Compute the dual norm of the L1 norm. (Here v · w denotes the inner product between v and w: v · w , Pn i=1 viwi) Solution: We will prove that sup kwk1≤1 (v · w) = max i2[n] vi = kvk1 (3) which implies that the dua...

Problem 2.1: Rather than doing the details of the convolution, we simply sketch the shapes of the waveforms. For a signal s = sc + jss and a filter h = hc + jhs, the convolution y = s ∗ h = (sc ∗ hc − ss ∗ hs) + j(sc ∗ hs + ss ∗ hc) For h(t) = smf (t) = s(−t), rough sketches of Re(y), Im(y) and |y| are shown in Figure 1. Clearly, the maximum occurs at t = 0. = c*hc −ss*hs Re(s* h) sc*hs ss*hc Im(s* h) |s* h| + = + s Figure 1: The convolution of a signal with its mat...

Exam (elaborations) TEST BANK FOR Fundamentals of Digital Communication By Upamanyu Madhow (Solution Manual) Solutions to Chapter 2 Problems Fundamentals of Digital Communication Problem 2.1: Rather than doing the details of the convolution, we simply sketch the shapes of the waveforms. For a signal s = sc + jss and a filter h = hc + jhs, the convolution y = s ∗ h = (sc ∗ hc − ss ∗ hs) + j(sc ∗ hs + ss ∗ hc) For h(t) = smf (t) = s(−t), rough sketches of Re(y), Im(y) and |y|...

Introduction To Linear Algebra

Introducción al Álgebras con Vectores en espacios vectoriales de R2 y R3, con explicaciones, ejemplos y ejercicios sobre las distintas operaciones entre vectores. Incluyendo la definición de Teoremas, demostraciones, propiedades e interpretaciones