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Unformatted text preview: 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 ]) = & , 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 ) ? 4. A child is with her father at a supermarket in front of t di/erent candy bar dispensers, each with k candy bars in it, each candy bar selling for a quarter. The child&s father gives her m quarters. In how many ways can she select m di/erent candy bars? 5. John tosses a fair die twice. (Note that there are 36 equally likely outcomes). ( i ) If Z denotes the sum of the two numbers obtained in the two tosses, compute P ([ Z = k ]) ( ii ) Find the probability that Z takes a value in this set: f a 1 ; ;a r g ....
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