(a)The following pattern classes have Gaussianprobability density functions.w; = { (0, 0)", (2, 0)" , (2, 2)" , (0, 2) "}and w2 = { (4, 4)" , (6, 4)" , (6, 6)", (4, 6)" }(i)1Assuming that p(w;) = p(w2)= 2obtain the equation of the Bayesdecision boundary between these twoclasses.(ii) Sketch the boundary.

Answered: Image /qna-images/answer/5d79d1ab-c634-4eda-8465-eff04750d319.jpg

Answered: (a) The following pattern classes have…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let fx(2.y) -{ 0.5ye zE(0. 0). y e (0,2) be the joint probability function of the random vector (X,Y). Which of the following statement is INCORRECT? elsewhere O X and Y are uncorrelated. O E(Y) = 1 O E(aX + bY) = aE(X)+ bE(Y), where a and b are constants. O E(X) = 1
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1. Determine the values (up to 4 decimal place) of the following: a. E(Y) = b. V(Y) = 2. Determine P(X >1.8, Y > 4.7) = 3. Determine P(Y <3) =
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Q. 2 There are two alternative routes for a ship passage. The sailing times for the two routes are two continuous random variables X and Y that have the joint density function fry(x, y) = {K e-0.5(y-*+3); 5 x – 3 0; e. w. (i) Obtain K so that it is the joint probability density function; (ii) Find the following probabilities (a) P(X < Y), (b) P(X 2 Y), (c) P(X +Y 2 1)
Question 1 Let X be a continuous random variable taking values in [a, b] with c.d.f. Fx which is strictly increasing on [a, b]. (a) Show that the random variable Fx(X) has a uniform distribution on [0, 1]. (b) Let U be a uniform random variable on [0, 1]. What is the distribution of the random variable F¹(U), where Fx¹ is the inverse of Fx? (c) Suppose that U1, U2, . Un are a set of computer-generated pseudo-random numbers (assumed to be drawn from a uniform distribution on [0, 1]). How would you use them to simulate a random sample X₁, X2,..., Xn from the distribution with density f(x) = = με-μα, x ≥ 0?

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