Fall 2000 Solutions

# Fall 2000 Solutions - ANSWERS TO FALL 2000 FINAL EXAM 1(a 1...

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ANSWERS TO FALL 2000 FINAL EXAM 1. (a) 1 6 4 (b) 5 (4) 6 4 (c) 6 (4) Ã 5 2 ! 1 6 5 2. (a) i) Ã 10 x ! ³ 2 5 ´ x × ³ 3 5 ´ 10 x , x =0 ,..., 10 ii) ³ 3 5 ´ y 1 × 2 5 , y =1 , 2 , 3 ,... (b) i) Ã 6 x 9 10 x ! Ã 15 10 ! , x 6 ii) 9 ( y 1) 15 ( y 1) × 6 16 y , y 10 c) i) 12! x 1 ! x 2 ! x 3 ! ³ 6 20 ´ x 1 ³ 9 20 ´ x 2 ³ 5 20 ´ x 3 , x i 0 , i , 2 , 3 , x 1 + x 2 + x 3 =12 . ii) Ã 12 y ! ³ 15 20 ´ y ³ 5 20 ´ 12 y , y 12 . 3. (a) θ> 0 (b) F ( x )= ( 0 ,x < 1 1 x θ 1 (c) 1 2 θ (d) θ θ 1 , 1 (e) θe θy , y 0 4. (a) x 01 y 012 f 1 ( x ) 0.4 0.6 f 2 ( y ) 0.4 0.3 0.3 (b) 0.56 (c) T 0123 g ( t ) 0.16 0.38 0.26 0.20 (d) P { X = x | T =2 } = ( 10 / 26 16 / 26 (e) 0.0491 (f) not independent since ρ 6 . 5. (a) 1 61 e 10 (b) Ã 9 2 ! (61 e 10 ) 3 (1 61 e 10 ) 7 (c) Ã 1000 5 ! (61 e 10 ) 5 (1 61 e 10 ) 995 (d) e µ µ 5 5! , µ = 1000 × 61 e 10 6. (b) i) [1 p (1 t )] n ii) np , np (1 p ) 7. (a) 0.1587 (b) 9.8 (c) -7 (d) not independent since correlated (e) 385

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## This note was uploaded on 10/21/2010 for the course STAT 230 taught by Professor Various during the Fall '06 term at Waterloo.

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Fall 2000 Solutions - ANSWERS TO FALL 2000 FINAL EXAM 1(a 1...

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