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Suggested Solutions of Assignment 1

Suggested Solutions of Assignment 1 - THE UNIVERSITY OF...

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Unformatted text preview: THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1306 INTRODUCTORY STATISTICS (SEMESTER 1 2008/2009) Suggested Solution of Assignment 1 Question 1 (a) This corresponds to the events {(1,1,1),(2,2,2),(3,3,3),(4,4,4),(5,5,5),(6,6,6)}, so the number of ways is 6 . (b) The number of ways is 6 & 5 = 30 . (c) The number of ways is 5 & 4 = 20 where the number shown on the &rst dice is &xed. (d) In fact, the events in (a), (b) and (c) cannot occur at the same time. Thus, the total number of possible ways that the bishop calculated is 6 + 30 + 20 = 56 . Question 2 (a) & 7 2 ¡ = 21 : (b) & 4 2 ¡ = 6 : (c) & 3 1 ¡& 4 1 ¡ = 12 : Question 3 (a) & 1 2 4 ¡ = ¢ 1 2 £¢ 1 2 ¡ 1 £¢ 1 2 ¡ 2 £¢ 1 2 ¡ 3 £ 4! = ¢ 1 2 £¢ ¡ 1 2 £¢ ¡ 3 2 £¢ ¡ 5 2 £ 24 = ¡ 5 128 : & ¡ 3 3 ¡ = ( ¡ 3) ( ¡ 4) ( ¡ 5) 3! = ¡ 10 : (b) By expanding ¢ 1 + 1 4 £ 1 = 2 up to 4 terms, we have & 1 + 1 4 ¡ 1 = 2 = 1 + & 1 2 1 ¡& 1 4 ¡ + & 1 2 2 ¡& 1 4 ¡ 2 + & 1 2 3 ¡& 1 4 ¡ 3 + ¢¢¢ 1 = 1 +...
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