The number of mistakes made per page of typing is Poisson with mean 0. The prior...

 

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The number of mistakes made per page of typing is Poisson with mean 0. The prior probabilities that takes the values 1.0 and 1.5 are 0.4 and 0.6 respectively. Two decisions are posssible: do and d, where do accepts Ho and d rejects Ho. The loss that occurs when do is made and Ho is true is 0 and is 2 when H is true. Similarly, losses of 0 and 4 are incurred when decision d is made and H and Ho are true respectively. (a) What is the Bayes decision if 5 pages are sampled at random and the observed number of mistakes per page are 1, 0,2,1, 1. (b) Suppose that a random sample of size n is taken, a total of x mistakes are observed and the prior probabilities that takes the values of 1.0 and 1.5 are So and respectively. Find the posterior distribution of 0. Hence determine the decision with smaller expected loss with respect to the posterior distribution. The number of mistakes made per page of typing is Poisson with mean 0. The prior probabilities that takes the values 1.0 and 1.5 are 0.4 and 0.6 respectively. Two decisions are posssible: do and d, where do accepts Ho and d rejects Ho. The loss that occurs when do is made and Ho is true is 0 and is 2 when H is true. Similarly, losses of 0 and 4 are incurred when decision d is made and H and Ho are true respectively. (a) What is the Bayes decision if 5 pages are sampled at random and the observed number of mistakes per page are 1, 0,2,1, 1. (b) Suppose that a random sample of size n is taken, a total of x mistakes are observed and the prior probabilities that takes the values of 1.0 and 1.5 are So and respectively. Find the posterior distribution of 0. Hence determine the decision with smaller expected loss with respect to the posterior distribution.