(a) A random sample z = (x1,I2,. .. ,In) is available from a distri-bution specified apart from an unknown real parameter 0. Basedon a given prior distribution, the posterior density of 0 is p(0 | 2).Show that the Bayes estimate of 0 under the loss functionL(t, 0)(t- 0)?where t is any estimate of 0, is given by {E(0-1 | 2)}-1.Scanned with CamScanner(b) It is believed that the number of arrivals in a queue will follow aPoisson distribution with mean 0 rer hour. Obtain the likelihoodfunction for 0 given that the number of arrivals in the last n hourswere 21, 12,., Dn.(c) Deduce the posterior distribution of 0 when the prior distributionis Gamma(a, B) and write down its probability density function.(d) Show that the Bayes estimate of 0 under the loss function specifiedin part (a) is given bya + s - 1B+nwhere s =(e) Find the predictive distribution of y the number of arrivals in thenext hour.

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(a) A random sample z = bution specified apart from an unknown real parameter 0. Based on a given prior distribution, the posterior density of 0 is p(0 a). Show that the Bayes estimate of 0 under the loss function (*1, 12,.. .,n) is available from a distri- L(t, 0) = (t-0)2 where t is any estimate of 0, is given by {E(0-1 | )}-1. 1 Scanned with Camicanner (b) It is believed that the number of arrivals in a queue will follow a Poisson distribution with mean 0 per hour. Obtain the likelihood function for 6 given that the number of arrivals in the last n hours were 1, 22, .., n (c) Deduce the posterior distribution cf 0 when the prior distribution is Gamma(a, B) and write down its probability density function. (d) Show that the Bayes estimate of 0 under the loss function specified in part (a) is given by a +s - 1 B+n where s E i. (c) Find the predictive distribution of y the number of arrivals in the next hour.

(a) A random sample z = bution specified apart from an unknown real parameter 0. Based on a given prior distribution, the posterior density of 0 is p(0 a). Show that the Bayes estimate of 0 under the loss function (*1, 12,.. .,n) is available from a distri- L(t, 0) = (t-0)2 where t is any estimate of 0, is given by {E(0-1 | )}-1. 1 Scanned with Camicanner (b) It is believed that the number of arrivals in a queue will follow a Poisson distribution with mean 0 per hour. Obtain the likelihood function for 6 given that the number of arrivals in the last n hours were 1, 22, .., n (c) Deduce the posterior distribution cf 0 when the prior distribution is Gamma(a, B) and write down its probability density function. (d) Show that the Bayes estimate of 0 under the loss function specified in part (a) is given by a +s - 1 B+n where s E i. (c) Find the predictive distribution of y the number of arrivals in the next hour.

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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