Past Exam Answers_08-09 Spring_09-10 Fall

Past Exam Answers_08-09 Spring_09-10 Fall - (d) ( ) ( ) y x...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1301 PROBABILITY AND STATISTICS I Past Examination Numerical Answers (2008-2009 Spring) 1. (a) No (b) No (c) 3 1 2. (b) 0.01295 (c) 0.6178 (d) ( ) 4 , 0.3712 (e) $0.6565, $1.19 3. (a) 0.9928 (b) No (c) 2.8, 2.85 (d) 0.1788 4. (a) , ) 2 ( Exp ( ) 2 , 2 Γ (b) 0.7017 (c) No (d) () y y x f Y X 1 | | = , (e) y x < < 0 () ( ) > = . 0 if 0 , 0 if 1 2 z z e z F z Z 5. (a) (b) 2 2 χ W 2 (d) π , 4 (e) () 2 r r R = λ , 0 > r (2009-2010 Fall) 1. (b) 0.24 (c) 0.4667 (d) 0.5222 2. (a) 4 1 (b) () ( ) 2 0 , 3 4 4 8 1 2 < < + = x x x x f X ; () 2 0 , 8 3 2 < < = y y y f Y (c) 6 5 , 12 1 , No
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Unformatted text preview: (d) ( ) ( ) y x y y x y x f Y X &lt; &lt; + = , 3 2 | 2 (e) 9 5 y (f) 12 5 (g) 24 1 3. (b) 10, 38 (c) ( ) ( ) ( ) ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + − + + − + = 9 1 6 1 1 2 1 exp 1 2 , 2 2 2 2 , v uv v v u v u v u f V U , ∞ &lt; &lt; ∞ − v u , (d) ( ) ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − = 2 2 2 1 2 9 exp 1 1 t t t t M Z , 1 1 &lt; &lt; − t (e) 0.2071 4. (a) 1, n 1 1 − (b) ( ) 1 ℘ (c) 1, 1 (d) 0.2642 p. 1...
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