The number of minutes between successive bus arrivals at
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The number of minutes between successive bus arrivals at Alvin's bus stop is exponentially distributed with parameter e, and Alvin's prior PDF of e is !e(O) = { 100. O. if 0 E [0. 1/5]' otherwise. (a) Alvin arrives on Monday at the bus stop and has to wait 30 minutes for the bus to arrive. What is the posterior PDF. and the IAP and conditional expectation estimates of E>? (b) Following his Monday experience. Alvin decides to estimate e more accurately. and records his waiting times for five days. These are 30. 25. 15. 40. and 20 minutes, and Alvin assumes that his observations are independent. What is the posterior PDF, and the MAP and conditional expectation estimates of e given the five-day data?
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