ECE300 Communication Theory

Problem Set III: MAP and ML Decision Rules

1. Urn I contains R1 red balls and B1 blue balls, and Urn II contains R2 balls and B2

blue balls. A ball is selected at random from Urn I and put into Urn II. Then a ball

from Urn II is selected. Based on the color of the ball chosen from Urn II, we try to

guess the color of the ball that was chosen from Urn I. Consider both the MAP and

ML decision rules for this case.

Take parameter values R1 = 2, B1 = 7, R2 = 3; B2 = 7, and perform N = 105

trials. Write code to perform computations as indicated below using MATLAB (i.e.,

no “pencil and paper”), in terms of general parameter values, and then run your code

with the speciÖc parameter values given here. The only special function should use in

MATLAB is randi. You should determine and output the following information:

Summarize the parameters: R1; B1; R2; B2; N.

The MAP and ML decision rules (e.g., “Guess Red if Red, Blue if Blue” etc.).

The theoretical probability of error for MAP and ML.

The estimated probability of error (i.e., the fraction of the time the decision rule

is wrong), for MAP and ML.

Repeat the above now for the cases R1 = 4, B1 = 5, R2 = 3, B2 = 7 (still N = 105

).

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