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Unformatted text preview: IE 300 / GE 331 Spring 2009 Homework #7 Problem 1. The number of minutes between successive bus arrivals at Alvin’s bus stop is exponentially distributed with parameter Θ, and Alvin’s prior PDF of Θ is f Θ ( θ ) = ( 10 θ, if θ ∈ [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 MAP and conditional expectation estimates of Θ? (b) Following his Monday experience, Alvin decides to estimate Θ 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 Θ given the five-day data? Problem 2. The number Θ of shopping carts in a store is uniformly distributed between 1 and 100. Carts are sequentially numbered between 1 and Θ. You enter the store, observed the number X on the first cart you encounter, assumed uniformly...
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This note was uploaded on 09/08/2009 for the course GE 331 taught by Professor Negarkayavash during the Spring '09 term at University of Illinois at Urbana–Champaign.
- Spring '09