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FinalExamTemplate

# FinalExamTemplate - Mathematics 7 Template for...

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Mathematics 7 April 15, 2008 Template for Examination #1 1 . A box contains N tags numbered from 1 to N . In how many ways can I select k of the tags? 2 . There are b boys and a girls in a group that forms a line. How many boy-girl patterns can be formed if at one end of the line there must be a boy and at the other end there must be a girl? 3 . Evaluate v X k = u ( ak + b ) 4 . Consider the data set { x 1 , · · · , x s } , where x 1 = · , x 2 = · , · · · and x s = · . Compute ( i ) the sample mean, x , and ( ii ) the sample median, µ . ( iii ) s X i =1 | x i µ | and ( ii ) s X j =1 ( x i x ) 2 . 5 . Suppose a box contains m white balls and n black balls. Suppose I select w balls at random. What is the probability that there are z white balls in the sample? 6 . Suppose m X i =1 a i = t . Evaluate m X i =1 sa i . 7 . Evaluate ¡ N k ¢ . 8 . In a game in which there are M equally likely outcomes, suppose that an event E can occur in a of the equally likely individual outcomes, and an event F can occur in b equally likely individual outcomes. If these two events are disjoint, compute the probability that at least one of these events occurs. 9 . Solve problem 8 when the two events have exactly k individual out- comes in common. 10 . If A and B are independent events, and if P ( A ) = s and P ( B ) = t , compute the value of P ( A B ) . 11 . If A and B are events, and if P ( A B ) = c and if P ( B ) = d , compute P ( A | B ) . 12 . Suppose P ( D ) = e . Compute P ( D c ) . 1

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13 . Suppose A and B are independent events, where P ( A ) = u and P ( B ) = v . Compute P ( A B c ) . 14 . Suppose a box contains m + n + q tags. m of the tags are numbered a , n of the tags are numbered b and q of the tags are numbered c . A tag is drawn at random from the box. Let X denote the number on the tag drawn. ( i ) What is the range of X ? ( ii ) Find P ([ X = x ]) for all values of x in range ( X / ) . 15 . An urn contains three rags, numbered a , b and c . One selects 2 tags at random from the three. Let Z denote the sum of the numbers on the two tags selected. Find P ([ Z = z ]) for all values of z in range ( Z ) . Mathematics 7 Template for Exam 2 May 6, 2008 No calculators No scratch paper! 1. Let X be a random variable whose distribution is Bin ( n, p ) . ( i ) What is the range of X ? ( ii ) Find the density of X . ( iii ) Compute P ([ X k ]) . ( iv ) Compute P ([ a X b ]) . (Leave your answers as reduced fractions.) 2. If Z is a random variable whose distribution is Bin ( n, p ) , and if P ([ Z t ]) = β , compute P ([ Z t + 1]) . 3. An urn contains N tags numbered from 1 to N . Let Y denote the sum of the numbers of n of them selected at random. ( i ) What is the smallest number in range ( Y ) ? ( ii ) What is the largest number in range ( Y ) ?
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