Question: solve in 30 mins thanks (c) Poisson process: A group of renewable energy student have done a bachelor project where they among other things observed

solve in 30 mins thanks (c) Poisson process: A

solve in 30 mins thanks

(c) Poisson process: A group of renewable energy student have done a bachelor project where they among other things observed news on the price of electricity in the largest news channels. We will use their data to do inference on the frequency of these news items. i. The group observed 13 items in the largest news channels during the last 5 months of 2021. Use this observation together with neutral prior hyperparameters for the Poisson process to find a posterior probability distribution for the rate parameter A, the mean number of such news items per month. ii. What is the probability that there will be precisely 3 such news items next month? iii. Find the probability distribution for T+2, the waiting time for the next 2 such news items, and calculate a 90% interval estimate ("predictive interval") for T+2

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