2. The frequency of heavy rains in one week follows a Poisson distribution with parameter A. According the past years, the rate )~ Unif{1,2,3, 4, 5, 6}. In the past 4 weeks, we have observed 4, 6, 5, 3. We want to give a proper estimate of A. Let X denote the frequency of heavy rains in one week. Please answer the following questions. (a) Find the joint probability of the data points 4,6, 5, 3 when A = j. (b) With the observed data points 4,6, 5, 3, please find the conditional distribution of A, p(A\data), subject to a constant. (Hint: p(X\data) x p(data|A)p(A), where p(data|X) is calculated in part (a) and p(X) is uniform on {1,2, 3, 4, 5, 6}.) (c) With the previous results, write a pseudo-code for p(\|data). (Hint: one way is to use the rejection algorithm for the kernel function. You can also identify the exact probabilities and use inverse method or table method.)
2. The frequency of heavy rains in one week follows a Poisson distribution with parameter A. According the past years, the rate )~ Unif{1,2,3, 4, 5, 6}. In the past 4 weeks, we have observed 4, 6, 5, 3. We want to give a proper estimate of A. Let X denote the frequency of heavy rains in one week. Please answer the following questions. (a) Find the joint probability of the data points 4,6, 5, 3 when A = j. (b) With the observed data points 4,6, 5, 3, please find the conditional distribution of A, p(A\data), subject to a constant. (Hint: p(X\data) x p(data|A)p(A), where p(data|X) is calculated in part (a) and p(X) is uniform on {1,2, 3, 4, 5, 6}.) (c) With the previous results, write a pseudo-code for p(\|data). (Hint: one way is to use the rejection algorithm for the kernel function. You can also identify the exact probabilities and use inverse method or table method.)
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter1: Foundations
Section1.3: Add And Subtract Integers
Problem 263E: Explain why the sum of 8 and 2 is negative, but the sum of 8 and 2 is positive.
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Could you please help with 2(a), 2(b) and 2(c). Thanks
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