For the Normal-Cauchy Bayes estimator:8(x) =5⁰⁰ง-e-(x-9) ²/² dv-∞0⁰ 1 +92 e1∞ 1 +9²e−(x−v)² dvBuild an Accept-Reject algorithm based on the Cauchy candidate to generate a samplefrom the posterior distribution and then deduce the estimator.

In this problem, we are dealing with a normal-cauchy Bayes estimator, , used to estimate a parameter…

Answered: For the Normal-Cauchy Bayes estimator:…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Two movie theaters compete for the business of 1,000 customers. Assume that each customer chooses between the movie theaters independently and with "indifference." Let N denote the number of seats in each theater. (a) Using a binomial model, find an expression for N that will guarantee that the probability of turning away a customer (because of a full house) is less than 1%. (b) Use the normal approximation to get a numerical value for N.
At an art store, the mean sale amount is $1250 per customer. The owner thinks that the mean sales amount increases during promotion. A random sample of 45 paintings purchased during a promotion was selected, the sample mean sales amount is x¯=1315. Assume σ=$155. How can I implement the hypothesis test to check if the mean sales amount increases during promotion, and let α=0.01. I want to solve by both P-value method and reject region method.
For a random variable, its hazard function also referred to as the instantaneous failure rate is defined as the instantaneous risk (conditional probabilty) that an event of interest will happen in a narrow span of time duration. For a discrete random variable X, its hazard function is defined by the formula hX(k) =P(X=k+ 1|X > k) =pX(k)1−FX(k). For a Poisson distribution with λ= 4.2, find hX(k) and use R to plot the hazard function.
state whether or not this resulting observed interval ended up capturing the true population proportion p of 0.45.
You obtain 336 successes in a sample of size n1=391n1=391 from the first population. You obtain 419 successes in a sample of size n2=472n2=472 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample
Let X11 X12, Xini and X21, X22, X2n2 be two independent random samples of size n₁ and n₂ from two normal populations N(₁, 2) and N(2, 2) respectively. (a) Derive the maximum likelihood estimators (mle's) of all the parameters in the first population (X₁). Using analogy, state the mle's of the parameters of the second population. (b) Find the pooled estimator of the common variance when it is assumed that of = = ². Suggest an unbiased estimator of o². |

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For the Normal-Cauchy Bayes estimator: ง 001 +92 8(x) = e-(x-9)²/2 dv % 1 -∞ 1 +9² Lo e-(x-9)² dv Build an Accept-Reject algorithm based on the Cauchy candidate to generate a sample from the posterior distribution and then deduce the estimator.