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26-03-2024
Mathematics

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Suppose that the annual percentage interest from an investment portfolio follow a normal distribution, with an unknown mean µ but known variance δ2 = 25. You are interested using Bayesian inference for estimating µ and providing an uncertainty estimate for it. A conjugate normal prior with mean m=8% and δ2 = 2.5 is to be used to represent the prior information.
(a) Suppose an i.i.d. random sample of m=4 previous years had sample mean of 6% annual percentage interest. Calculate the maximum likelihood estimate of the level of interest in the lowest 5% of all years, i.e. the percentage loss (or worst gain) you expect to get every 20 years. You must use R to calculate it.

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