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| − | + | Consider <math class="inline">n</math> independent flips of a coin having probability <math class="inline">p</math> of landing on heads. Say that a changeover occurs whenever an outcome differs from the one preceding it. For instance, if <math class="inline">n=5</math> and the sequence <math class="inline">HHTHT</math> is observed, then there are 3 changeovers. Find the expected number of changeovers for <math class="inline">n</math> flips. ''Hint'': Express the number of changeovers as a sum of Bernoulli random variables. | |
:'''Click [[ECE_PhD_QE_CNSIP_2013_Problem1.1|here]] to view student [[ECE_PhD_QE_CNSIP_2013_Problem1.1|answers and discussions]]''' | :'''Click [[ECE_PhD_QE_CNSIP_2013_Problem1.1|here]] to view student [[ECE_PhD_QE_CNSIP_2013_Problem1.1|answers and discussions]]''' | ||
Revision as of 15:55, 3 November 2014
Communication, Networking, Signal and Image Processing (CS)
Question 1: Probability and Random Processes
August 2013
Question
Part 1.
Consider $ n $ independent flips of a coin having probability $ p $ of landing on heads. Say that a changeover occurs whenever an outcome differs from the one preceding it. For instance, if $ n=5 $ and the sequence $ HHTHT $ is observed, then there are 3 changeovers. Find the expected number of changeovers for $ n $ flips. Hint: Express the number of changeovers as a sum of Bernoulli random variables.
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Part 2.
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Part 3.
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Part 4.
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