3. 11 mark(s) A paleontologist is trying to measure the age a (in millions of years) of a dinosaur skeleton. She constructs a large Bayes Box to work out the posterior distribution for a given some data. The Bayes Box columns are calculated by some R code contained in a file dinosaur R which you can download from Canvas. The code also plots the posterior distribution. (a) (4 mark(s) Find a 95% credible interval for a (include your code). (b) 2 mark(s) Find the posterior median for a (include your code). (c) (1 mark(s) The paleontologist is going to be interviewed on television about the dinosaur, and she needs to have a point estimate @ of the age so she can say it quickly rather than having to talk about the posterior distribution. She decides that the loss associated with stating a on TV when the true value is a is L= a - al. Find the value of the best point estimate . (d) (4 mark(s) Later, the paleontologist develops a new technique that works out the true value a with no uncertainty. Before applying it to this skeleton, she decides to throw a party if the true value is between 0.9 times and 1.1 times the point estimate from (c). Calculate the probability that she throws a party