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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Rework problem 18 from section 3.3 of your text, involving filling in missing probabilities on a tree diagram. Construct a copy of figure 3.11 in your text, where the first outcome is one of (A,B,C) and the second outcome in each case is one of (1,2,3) (only 1 or 2 in the case of outcome C). Use the following probabilities instead of those given in your text: Pr[A1] Pr[2|A] Pr[A2] Pr[A3] Pr[B1] Pr[2|B] Pr[B3] Pr[C1] Pr[C2] 12 1 12 12 1 1 12 Find the following missing probabilities: (1) Pr[A] = (2) Pr[1|A] (3) Pr[2|A] = (4) Pr[B] =
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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…
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Problem 2.5 (Video 1.5, 1.6, 2.1, 2.2, Quick Calculations) Calculate each of the requested quantities. (a) Let A and B be independent events with P[A] = 1/5 and P[B] = 1/4. Calculate P[An B] and P[AUB]. = (b) Let A₁, A2, A3 be events that are conditionally independent given B. Additionally, assume that A₁, A2, A3 are conditionally independent given Bc. Assume that P[A;|B] = 1/4 and P[AB] = 1/2 for i : 1, 2, 3 and P[B] = 1/3. Calculate P[A₁ A²A3|B] and P[A₁A²A3]. (c) Consider a packet of jellybeans that contains 9 jellybeans, of which 4 are lemon and the remaining 5 are raspberry. You reach in and pull out 3 jellybeans. What is the probability that they are all lemon? What is the probability that they are all raspberry? Calculate P[X # 0] (d) Let X be a random variable with PMF Px(x) = = and P[X>0|X ‡ 0]. (e) If the random variable Y has CDF Fy (y) = (1/6 x = -1, +1 |2/3 x=0 y < 1 1/4 1≤y<5, what is the PMF of Y? 5 ≤y
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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…
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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