For questions 1-7, assume theproblem is stated as follows: Wehave a binary detection problemwith two hypotheses: H and HWe observe a random variable y,0and we are given the conditionalprobabilities of y asY|Hf.Y|H1(y) = 0.5, y = [1,1]; 0 otherwise.(y) = 1 lyl, y = [1,1]; 0 otherwise.-0.5The two densities are shown in thefigures below.1614121OB0.60.4-0.20545120806041°02)05 QUESTION 4Now suppose that P (H ) =1/3,P(H₂) = 2/3Find the maximum a posteriori (MAP)decision rule. From the pictures, the MAPdecision rule should be to say H, for \Y\

Consider a binary detection problem with two hypotheses. Consider a random variable Y with…

Answered: For questions 1 -7, assume the problem…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Problem 3: Nerves and Conversation Dr Johnson is interested in testing the hypothesis that people talk more when they are nervous. She obtains 36 volunteers from undergraduate classes to participate in her experiment. She randomly assigned them to one of two conditions and scheduled a separate appointment time with each student. When a student in Group 1(Low Stress) arrives for their appointment they are told that in 10 minutes they will be asked to describe how friendly they are by completing a true-false personality measure. Students in Group 2 (High Stress) were told that in 10 minutes they will be asked a set of questions by a panel of measurement specialists to determine how friendly they are. In both groups the conversations between the waiting student and the experimenter were recorded for 10 minutes. During this waiting time, the experimenter made certain set comments if no conversation occurs during a one-minute interval, and consistently answers questions with brief…
Problem 5: A professor tries to count the number of students attending lecture in person. For each student in the audience, the professor either counts the student accurately with probability p or misses the student in the count with probability (1 – p). The exact number of attending students is 20. (a) The number of students counted by the professor is a random variable N. What is the PMF of N? (b) Let U = 20 – N denote the number of uncounted students. What is the PMF of U? (c) What is the probability that the undercount U is 2 or more? (d) For what value of p is E[U] = 2?
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Rework problem 7 from section 4.1 of your text involving the computation of probabilities for a Bernoulli trial. Assume that n = 9, and p = 5757. Find the probability of at least 1 success and at least 1 failure.
Questions 3 - 4 The weight of 7 football players in kilograms was recorded. The measurements are given below. Football Weight _player 1 68 2 81 3 79 70 80 74 7 70 3. Find the median. A. 76 77 78 B D 75 E 74 Find the standard deviation. 5.669 5.412 5.094 4. A в C 5.984 5.815 D
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Rework problem 7 from section 4.1 of your text involving the computation of probabilities for a Bernoulli trial. Assume that n = 9, and p = 710710. Find the probability of at least 2 successes and at least 2 failures
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For questions 1 -7, assume the problem is stated as follows: We have a binary detection problem with two hypotheses: H and H. H₁ We observe a random variable y, and we are given the conditional