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Computer Science 174 - Spring 1998 - Canny - Midterm 1

Computer Science 174 - Spring 1998 - Canny - Midterm 1 -...

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CS174 CS174 Spring 98 Feb24 J. Canny MIDTERM I This is a closed book exam with 5 questions. You are allowed to use the formula sheet that will be handed out with the exam. No other notes are allowed. Calculators are OK. Write all your answers in this booklet. The score for each question is shown alongside the question. Make sure you attempt all of them. Good Luck! •@ Name: _____________________________________ •@ •@ SID Number: _______________________________ •@ •@ •@ •@ 1.(20 points) Let a biased coin have Pr [Heads] = p , where p is not necessarily 0.5. This coin can still be used to simulate fair coin tosses by tossing it twice, where if the actual sequence of tosses is HT, the output is "H", while if the actual sequence of tosses is TH, the output is "T". If the actual tosses are both the same, repeat the process. Let an "event" be a pair of tosses, and let the random variable X count the number of events until "h" or "T" is output, including the last, so X >= 1. file:///C|/Documents%20and%20Settings/Jason%20Raft...%20Spring%201998%20-%20Canny%20-%20Midterm%201.htm (1 of 3)1/27/2007 6:46:39 PM
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