assn3 - Math 361, Problem set 3 Due 9/20/10 1. (1.4.21)...

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Math 361, Problem set 3 Due 9/20/10 1. (1.4.21) Suppose a fair 6-sided die is rolled 6 independent times. A match occurs if side i is observed during the i th trial, i =1 , . . . , 6. (a) What is the probability of at least one match during on the 6 rolls. (b) Extend part ( a ) to a fair n -sided die with n independent rolls. Then determine the limit of the probability as n →∞ . 2. (1.4.32) Hunters A and B shoot at a target; their probabilities of hitting the target are p 1 and p 2 respectively. Assuming independent, can p 1 and p 2 be chosen so that P (0 hits) = P (1 hit) = P (2 hits)? 3. (1.5.1) Let a card be selected from an ordinary deck of playing cards. The outcome c is one of these 52 cards. Let X ( c ) = 4 if c is an ace, let X ( c ) = 3 if c is a king, X ( c ) = 2 if c is a king and X ( c ) = 1 if c is a jack. Otherwise X ( c ) = 0. Suppose P assigns a probability of 1 52 to each outcome c . Describe the induced probability P X ( D ) on the space D = { 0 , 1 , 2 , 3 , 4 } of the random variable
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assn3 - Math 361, Problem set 3 Due 9/20/10 1. (1.4.21)...

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