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3. You are given: (i) Individual claim sizes follow a normal distribution with mean p. and standard deviation 100. (ii) The prior distribution of p, follows a normal distribution with mean 1000 and standard deviation 100. (iii) One claim of 1020 was observed. (a) Derive the probability density function of the posterior distribution of [1,, via the likelihood function and the prior probability density function, to show that the posterior distribution of u is normal with mean 1010 and variance 5000. (b) Determine the 95% highest posterior density credible interval for a. Make sure you conceptually understand the meaning of a highest posterior density credible interval before attempting to answer this