11_30_09 - ignition are stolen. On the other hand, only...

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STAT 409 Examples for 11/30/2009 Fall 2009 1. A statistics instructor teaches two statistics classes, one in the morning and one in the afternoon. Suppose the probability that the instructor gives a good morning lecture is 0.3. If the morning lecture is good, then the afternoon lecture is also good with probability 0.70. However, if the morning lecture is bad, then there is an 80% chance that the afternoon lecture will also be bad. a) What proportion of the afternoon lectures are bad? b) What is the probability that at least one lecture is bad (i.e., either morning lecture is bad or the afternoon lecture is bad, or both)? c) If at the conclusion of the afternoon class, the instructor is heard to mutter “what a rotten lecture,” what is the probability that the morning lecture was also bad? 2. In Anytownville, 10% of the people leave their keys in the ignition of their cars. Anytownville’s police records indicate that 4.2% of the cars with keys left in the
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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.

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11_30_09 - ignition are stolen. On the other hand, only...

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