TA3 - ECO2121: Methods of Economic Statistics TA3 – 4...

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Unformatted text preview: ECO2121: Methods of Economic Statistics TA3 – 4 February 2009 1. Conditional Probability Recall Pr{ A ∪ B } = Pr{ A } + Pr{ B } – Pr{ A ∩ B } Pr{ A ∩ B } = 0 if A and B are mutually exclusive. Suppose not, Pr{ A ∩ B } can be calculated first by conditioning on either event, i.e. Pr{ A ∩ B } = Pr{ A | B } × Pr{ B } or Pr{ A ∩ B } = Pr{ B | A } × Pr{ A } rearranging, Pr{ A | B } = Pr{ A ∩ B } / Pr{ B } or Pr{ B | A } = Pr{ A ∩ B } / Pr{ A } Hence, Pr{ A | B } = Pr{ A } and Pr{ B | A } = Pr{ B } if A and B are independent, which gives the usual formula Pr{ A ∩ B } = Pr{ A } × Pr{ B } Example: the probability of getting tail in tossing a coin and 6 in throwing a dice, given the coin and the dice are both fair and independent can be calculated as Pr{tail | 6} × Pr{6} = Pr{tail} × Pr{6} = 1/2 × 1/6 = 1/12 Bayes ’ Theorem: Given { B i } i=1, … ,k is a partition, for any (observed) event A, ∑ = × × = = k j j j i i i i B B A B B A A A B A B 1 } Pr{ } | Pr{ } Pr{...
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This note was uploaded on 11/16/2009 for the course ECO 2121 taught by Professor Professorwen during the Fall '08 term at Al Ahliyya Amman University.

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TA3 - ECO2121: Methods of Economic Statistics TA3 – 4...

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