4.3 The following pattern classes have Gaussian probability density functions:w:{(0,0), (2,0), (2, 2), (0, 2)) and w₂:{(4,4), (6,4), (6, 6), (4, 6)¹}.(a) Assume that P(W₂₁) = P(W₂) =2boundary between these two classes.(b) Sketch the boundary.and obtain the equation of the Bayes decision

We have been given the Gaussian Probability Density Functions. We have to obtain the equation of the…

Answered: 4.3 The following pattern classes have…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A joint probability mass function (pmf) is given by рх,у (—3, 0) — 0.18, Рx,у (-2, 1) — 0.08, рх,у (—1,4) — 0.16, рх,у (0,0) — 0.14, PX,Y (1, 2) = 0.04, рх,у (2, 1) — 0.4 The value of P(X >-1,Y > 1) is
Question 34. Let X be a random variable with probability density function Sžr², re (0,3), f(r) = else. Which of the following statements are correct? I a) The expected value of X is . b) The probability of X < 1 is . c) The probability of X € [0,0.5] is . d) The probability of X = 1 is zero.
2. Let X and Y be two independent exponential random variables with parameters both equal to 3. (a) Find f(x, y), the joint probability density function of X and Y. (b) Let A = {(x, y) = R² : x > 4 and y > 5}. Find P(A). (c) Let B = {(x, y) = R² : x + y ≤ 2}. Find P(B).
Q. 4 Let X and Y be two continuous random variables with following joint probability density function SK (x² + y²); 0 Y), (c) P(X +Y > 1) (b)
4.) The density function of X is (2x, f(x) .0, (a) Find the mean E(3X+1); (b) Find the variance 04x+5². 0 < x < 1, elsewhere.
9) 2.
4
Q3
3. Let random variables X and Y be independent with joint density fe(x, y). Let Ix (0) and Iy (0) be the Fisher information of X and Y, respectively. Prove that the Fisher information I(x,y)(0) = Ix(0) + Iy(0).
Assume that S={O1, O2, O3, O4} and that w1 = 0.22, w2 = 0.12, w3 = 0.17, w4 = 0.49. Let E={O2, O3} and F={O3, O4}. (a) What is the probability Pr[E]? (b) What is Pr[F′]? (c) What is Pr[(E∪F)′]?
a) Write down an expression for the probability density, ρ(t, x), in terms of the wavefunction of a particle, Ψ(t, x). b) Write down expressions for the momentum and energy operators, pˆ and Hˆ , for a particle in one dimension. c) Write down expressions for the expectation values of momentum and energy, ⟨p⟩ and ⟨E⟩, for the wavefunction Ψ(t, x). d) Write down an expression for the uncertainty in momentum, ∆p, in terms of the relevant expectation values.
5) The joint probability density function of X and Y is: fxy(x, y) = {K (x + y), 0, a) Find Fxy(x, y). b) Find fx|y(x | y). c) Find Fxy(x|y). 0 ≤ x ≤ 1 and 0 ≤ y ≤ 2 elsewhere

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