Question

Problem 1 (100/70): In a 1-D, 2-class problem, the density functions of both classes are adequately represented by univariate Gaussians, with μ1-4, σ1-2 μ2-6 σ2-3. (1) (15/10) Sketch the two density functions on the same figure using pencil and paper (i.e., without MATLAB or any other software package). Assume equal prior probability, predict how many decision regions there would be. (2) (55/30) Assume equal prior probability, (10/5) Ifr-4.7, which class does r belong to? Use the MAP method. Show detailed steps. (15/10) Find the decision boundary using analytical methods instead of the sketch. (10/5) Write an expression for the probability of error plerror |o that an error occurs given that the truth is class l (20/10) Solve for the overall probability of error. a. b. c. d. (3) (30/20) Assume that P(o)-0.6. P(on)-0.4. (20/10) Use MATLAB to draw the pdf and the posteriori probability Comment on the difference (5/5) Redo question 2 (a) (5/5) Under what condition that there would just be one decision region and two decision regions? a. b. c.

Answer 1

て 10