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1. The random variable z describes the observation of a physical phenomenon whose statistical description depends of one of two hypotheses. Conditioned on hypothesis H₁, the random variable z is Erlang (3,0.1), while conditioned on hypothesis Ho, the random variable z is Erlang (1,0.1). If Pr{H} = 0.65, and Pr{H} = 0.35, a) develop the likelihood ratio to implement a MAP decision test in order to decide between the two hypotheses. b) Obtain the probability of error of the test. c) If z=15.5, what decision results from the test?

1. The random variable z describes the observation of a physical phenomenon whose statistical description depends of one of two hypotheses. Conditioned on hypothesis H₁, the random variable z is Erlang (3,0.1), while conditioned on hypothesis Ho, the random variable z is Erlang (1,0.1). If Pr{H} = 0.65, and Pr{H} = 0.35, a) develop the likelihood ratio to implement a MAP decision test in order to decide between the two hypotheses. b) Obtain the probability of error of the test. c) If z=15.5, what decision results from the test?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 19E
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1. The random variable z describes the observation of a physical phenomenon whose statistical description depends of one of two hypotheses. Conditioned on hypothesis H₁, the random variable z is Erlang (3,0.1), while conditioned on hypothesis Ho, the random variable z is Erlang (1,0.1). If Pr{H}} = 0.65, and Pr{H} = 0.35, a) develop the likelihood ratio to implement a MAP decision test in order to decide between the two hypotheses. b) Obtain the probability of error of the test. c) If z=15.5, what decision results from the test?
Transcribed Image Text:1. The random variable z describes the observation of a physical phenomenon whose statistical description depends of one of two hypotheses. Conditioned on hypothesis H₁, the random variable z is Erlang (3,0.1), while conditioned on hypothesis Ho, the random variable z is Erlang (1,0.1). If Pr{H}} = 0.65, and Pr{H} = 0.35, a) develop the likelihood ratio to implement a MAP decision test in order to decide between the two hypotheses. b) Obtain the probability of error of the test. c) If z=15.5, what decision results from the test?
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