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Unformatted text preview: ignition are stolen. On the other hand, only 0.2% of the cars without keys left in the ignition are stolen. Suppose a car in Anytownville is stolen. What is the probability that the keys were left in the ignition? 3. Let p denote the probability of obtaining tails for a particular coin. The prior probability distribution of p is P ( p = 0.50 ) = 0.80, P ( p = 0.40 ) = 0.20. Find the posterior distribution of p , given that we observe 7 tails in 20 tosses. 4. Suppose that S = { 1, 2 }, Ω = { 1, 2, 3 }, and the class of probability distribution for the response s is given by the following table. s = 1 s = 2 f 1 ( s ) 1/2 1/2 f 2 ( s ) 1/3 2/3 f 3 ( s ) 3/4 1/4 If we use the prior π ( θ ) given by the table θ = 1 θ = 2 θ = 3 π ( θ ) 1/5 2/5 2/5 then determine the posterior distribution of θ for each possible sample of size 1....
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This note was uploaded on 10/12/2011 for the course STATISTICS stat 410 taught by Professor Stepanov during the Spring '11 term at University of Illinois, Urbana Champaign.
 Spring '11
 Stepanov
 Statistics, Probability

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