Consider a sample of claim counts per month of size 12. For the first 6 months,...

Transcribed Image Text:

Consider a sample of claim counts per month of size 12. For the first 6 months, the number of claims follows Poisson with mean 2. For the remaining 6 months, the number of claims follows Poisson with mean 1.52. (a) Show that 1(2; x) =12xln 2-152+c(x) for which c(x) is a function that depends only on the sample but not on 2. (b) Hence, express the MLE for in terms of the sampled values. (c) Show that E(X)= 1.252. Hence, express the Fisher information in terms of 2. Consider a sample of claim counts per month of size 12. For the first 6 months, the number of claims follows Poisson with mean 2. For the remaining 6 months, the number of claims follows Poisson with mean 1.52. (a) Show that 1(2; x) =12xln 2-152+c(x) for which c(x) is a function that depends only on the sample but not on 2. (b) Hence, express the MLE for in terms of the sampled values. (c) Show that E(X)= 1.252. Hence, express the Fisher information in terms of 2.

Answer rating: 100% (QA)

a To show that 1 x 12x ln 1151cx we need to use the likelihood function for a Poisson distribution The likelihood function for a Poisson distribution ... View the full answer