04spfinan - 2(a E X = 0 E Y = 2 3(b The correlation is 0(c...

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Answers to 2004 Spring Semester Sample Final Exam M´arton Bal´azs 1. The expected number of dark intervals is ( n - 1) p 2 . The variance is p 2 (1 - p ) · [( n - 1)(1 + p ) + 2( n - 2) p ]. 2. (a) r = r 3 7 . (b) E ( X | Y = y ) = y - 1 ln y . 3. 0 . 0455 or 0 . 0436, depending on whether we use the “midpoint between integers” trick or not. 5. f ( y ) = λ y λ +1 for y > 0, and zero elsewhere. 6. 0.124. Answers to 2004 Spring Semester Final Exam 1. The expected number of names is 9.58, the standard deviation is 0.596.
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Unformatted text preview: 2. (a) E ( X ) = 0, E ( Y ) = 2 3 . (b) The correlation is 0. (c) E ( X | Y = y ) = 0, E ( Y | X = x ) = 1+ | x | 2 . 3. . 1056. 4. (a) The probability is 1 2 . (b) The conditional probability is i 45 . 5. The expectation is 1 4 (mile), the variance is 1 48 (mile 2 ). 6. The probability that Mr. B has to wait is 3 4 ....
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