Suppose that1X\µ ~ Bernoulli(1+e-(u+2)and a standard normal N(0, 1) prior is specified for u. In a trial, the valuex = 1 is observed.(a) Show that the posterior for u when X is observed to be r = 1 isf(4x = 1) x (1+e¯(u+2)-le¬w²/2 on R.This posterior distribution cannot be sampled from directly. Suppose thatthe Metropolis-Hastings algorithm is to be used to simulate samples fromthe target posterior density f(H|r = 1).In order to simulate samples from the posterior distribution of parameter u,consider the sequence of random variables u1, #2, - such that µt is thevariable for iteration t of the Metropolis-Hastings algorithm. Let be itssimulated value. Suppose that the proposal distribution for +1H = Hewhich has density denoted by q(H+1\44), is N(µ,2).%3D

The random variable which has an integer value is called a discrete random variable. The Bernoulli…

Answered: Suppose that 1 1+e-(+2) Xu Bernoulli (…

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.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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Let x be a random variable representing dividend yield of German bank stocks. We assume that x has a normal distribution with average = 4.7% with SD = 2.4%. My random sample of 64 dividend yields of German bank stocks from the South of Germany had an average of 5.4%. Test if my sample of German bank stocks from the South are statistically different from the rest of Germany. For this test use the critical value of Zc = +-1.96 and and alpha = 0.05. Determine the null and alternative hypothesis. Group of answer choices H0 : population average = 4.7% H1 : population average > 4.7% H0 : population average = 4.7% H1 : population average 4.7% H0 : population average = 5.4% H1 : population average < 5.4% H0 : population average = 5.4% H1 : population average 5.4% For this test use the critical value of Zc = +-1.96 and and alpha = 0.05. Determine the test statistic. Group of answer choices z = -2.33 z = +2.33 z = -0.29 z = +0.29 For this test use the critical value of Zc = +-1.96 and…

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Suppose that 1 1+e-(+2) Xu Bernoulli ( and a standard normal N(0, 1) prior is specified for u. In a trial, the value x= 1 is observed. (a) Show that the posterior for when X is observed to be r= 1 is ƒ(μ\x= 1) x (1 + e-(μ+2))-¹-²/2 on R.