Example class 2

Example class 2 - Department of Statistics and Actuarial...

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Unformatted text preview: Department of Statistics and Actuarial Science STAT1301 Probability and Statistics I Example Class 2 1. A business man has 100 units of money. He wants to buy 4 dierent stocks. How many ways can he invest in such a way that he buys at least one unit of money of each stocks and each piece costs exactly 1 unit of money? Answer: total number of ways is number of solutions to the following model: X1 + X2 + X3 + X4 = 100; Xi > 0 which is 100 1 . 4 1 2. Two fair dice are thrown n times, compute the probability The sum of two dice is 7 on the nth throw for the rst time Sum 7 appears exactly 2 times among n throws Sum 7 appears at most 2 times among n throws Answer: Possible combinations which result to sum 7 are: f(1; 6); (2; 5); (3; 4); (4; 3); (5; 2); (6; 1)g, thus 30=36 30=36 30=36 6=36 = (5=6)n 1 (1=6) n (5=6)n 2 (1=6)2 n (5=6)n 2 (1=6)2 + n (5=6)n 1(1=6) + (5=6)n 2 2 1 3. Two integers are selected with replacement from rst 10 digits f1; 2; ; 10g. What is the probability that sum of them is odd? Answer: Total number of ways=10 10 = 100, # sum is odd= 5 5 20, 1 1 50 P(sum of two selected numbers are odd)= 100 1 4. In a game you draw 5 balls which are numbered 1 to 100 without replacement from a box and write down the numbers, and return back the balls into the box. If for the second time you draw 3 balls from the box, what is the probability that you draw at least one of the balls you have drawn in rst time? Answer: # of favourite outcomes= 100 95 , 3 3 P(at least one of the balls in second draw is the same as rst draw) 100 95 = ( 3() ( 3 ) = 10099989995989493 % :14 100 100 ) 3 2 ...
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This note was uploaded on 04/29/2010 for the course STAT 1301 taught by Professor Smslee during the Spring '08 term at HKU.

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Example class 2 - Department of Statistics and Actuarial...

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