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2. 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 Gaussian (200,10), while conditioned on hypothesis Ho, the random variable z is Gaussian (150,10). If Pr{H}=0.1, and Pr{H}=0.9, 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=165, what decision results from the test?

2. 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 Gaussian (200,10), while conditioned on hypothesis Ho, the random variable z is Gaussian (150,10). If Pr{H}=0.1, and Pr{H}=0.9, 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=165, what decision results from the test?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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2. 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 Gaussian (200,10), while conditioned on hypothesis Ho, the random variable z is Gaussian (150,10). If Pr{H}} = 0.1, and Pr{H}=0.9, 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=165, what decision results from the test?
Transcribed Image Text:2. 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 Gaussian (200,10), while conditioned on hypothesis Ho, the random variable z is Gaussian (150,10). If Pr{H}} = 0.1, and Pr{H}=0.9, 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=165, what decision results from the test?
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