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SampleMidterm

SampleMidterm - STAT511 Exam 1 Summer 2008(50 pts I...

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STAT511 Exam 1 Summer 2008 (50 pts) I. Multiple choice 1. Which of the following is not correct? A Mutually exclusive events must be independent events B P ( A B ) P ( A ) C Axioms of probability say that for two events A 1 and A 2 are mutually exclusive, we have P ( A 1 A 2 ) = P ( A 1 ) + P ( A 2 ). D None of the above is correct 2. P ( A 1 ) = 4 / 5, P ( A 2 ) = 1 / 5, A 1 and A 2 are mutually exclusive events. Suppose we know P ( B | A 1 ) = 1 / 10 and P ( B | A 2 ) = 1 / 5, find P ( A 2 | B ). ( Hint: Bayes ) A 1 4 B 1 3 C 1 12 D 1 7 3. X Exp ( λ = 5), what is the probility of X > 3? A 1 - e - 15 . B 1 - 3 e - 15 C 3 e - 15 D e - 15 . 4. A deck of 52 cards, take 4 out without replacement one by one. We saw that the first card is a club, now what is the probability that second is a heart? A 1 4 B 13 51 C 13 2 52 · 51 D None of the above 5. X U (2 , 5), what is E ( X 2 )? A 7 2 B 13 C 3 4 D None of the above 6. For the standard normal distribution, which of the following is not correct? A The density function is f ( z ) = 1 2 π e - z 2 / 2 , -∞ < z < B Mean is 0 and variance is 1.

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