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Question 1: Data For the geometric model of exercise sheet 5, question 2, suppose that for a prior distribution, we assign a Beta(a, 3) distribution. We take a = 1 and choose ß so that the prior probability P(q≤ 0.4) is 0.9. (a) Find the value of 3 that satisfies this requirement. (b) Use R to simulate a large sample from this beta distribution, and so check your calculation.

Question 1: Data For the geometric model of exercise sheet 5, question 2, suppose that for a prior distribution, we assign a Beta(a, 3) distribution. We take a = 1 and choose ß so that the prior probability P(q≤ 0.4) is 0.9. (a) Find the value of 3 that satisfies this requirement. (b) Use R to simulate a large sample from this beta distribution, and so check your calculation.

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.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 1E
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please answer asap using r code and showing the method. you need to refer to the bottom question and the dataset on the side but no need to answer question 2, just question 1a and 1b. thanks!

 

Question 1: Dataset: 3.807 For the geometric model of exercise sheet 5, question 2, suppose that for a prior distribution, we assign a Beta(a, 3) distribution. We take a = 1 and choose B so 2.264 that the prior probability P(q ≤ 0.4) is 0.9. 2.971 2.617 1.852 (a) Find the value of 3 that satisfies this requirement. 2.253 3.572 2.017 (b) Use R to simulate a large sample from this beta distribution, and so check your 1.991 calculation. 1.261 Question 2 Exercise Sheet 5: The column in the exercise sheet 5 dataset, labelled x, contains the observed data data be ₁,...,n. Suppose that each data-point x; is normally distributed, with unknown mean and standard deviation assumed to be equal to 1. As a prior distribution for 0, we assign a normal distribution with mean 5 and standard deviation 10. (a) What is the posterior distribution for 8? (b) What is the posterior mean for ? (c) What is the posterior median for 0? (d) What is a 95% equal tail credible interval for ? 1.925 2.539 1.122 2.788 2.356 3.508 2.541 2.317 2.021 3.177 1.163 1.775 2.006 2.604 2.553 2.65 4.313 1.478 2.41 2.683 3.563 2.413 2.692 3.055 1.778
Transcribed Image Text:Question 1: Dataset: 3.807 For the geometric model of exercise sheet 5, question 2, suppose that for a prior distribution, we assign a Beta(a, 3) distribution. We take a = 1 and choose B so 2.264 that the prior probability P(q ≤ 0.4) is 0.9. 2.971 2.617 1.852 (a) Find the value of 3 that satisfies this requirement. 2.253 3.572 2.017 (b) Use R to simulate a large sample from this beta distribution, and so check your 1.991 calculation. 1.261 Question 2 Exercise Sheet 5: The column in the exercise sheet 5 dataset, labelled x, contains the observed data data be ₁,...,n. Suppose that each data-point x; is normally distributed, with unknown mean and standard deviation assumed to be equal to 1. As a prior distribution for 0, we assign a normal distribution with mean 5 and standard deviation 10. (a) What is the posterior distribution for 8? (b) What is the posterior mean for ? (c) What is the posterior median for 0? (d) What is a 95% equal tail credible interval for ? 1.925 2.539 1.122 2.788 2.356 3.508 2.541 2.317 2.021 3.177 1.163 1.775 2.006 2.604 2.553 2.65 4.313 1.478 2.41 2.683 3.563 2.413 2.692 3.055 1.778
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Calculus For The Life Sciences
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