2.14 Exercises on Chapter 2
1. Suppose that 
. Find the standardized likelihood as a function of π for given k. Which of the distributions listed in Appendix A does this represent?
. Find the standardized likelihood as a function of π for given k. Which of the distributions listed in Appendix A does this represent?
2. Suppose we are given the 12 observations from a normal distribution:
15.644, 16.437, 17.287, 14.448, 15.308, 15.169,
18.123, 17.635, 17.259, 16.311, 15.390, 17.252,
and we are told that the variance 
. Find a 90% HDR for the posterior distribution of the mean assuming the usual reference prior.
. Find a 90% HDR for the posterior distribution of the mean assuming the usual reference prior.
3. With the same data as in the previous question, what is the predictive distribution for a possible future observation x?
4. A random sample of size n is to be taken from an 
distribution where 
is known. How large must n be to reduce the posterior variance of to the fraction 
of its original value (where k> 1)?
distribution where is known. How large must n be to reduce the posterior variance of to the fraction of its original value (where k> 1)?
5. Your prior beliefs about a quantity θ are such that
A random sample of size 25 is taken from ...
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