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Alfreda and Buzz each complete a five mile run every day. Over the course of 7...

Alfreda and Buzz each complete a five mile run every day. Over the course of 7 days, Alfreda finishes her run faster than Buzz exactly four times. Let p denote the true probability that Alfreda is a faster runner than Buzz, and suppose that the number of time Alfreda finishes first is binomially distributed. Determine the likelihood function L(p) and calculate the maximum likelihood estimator p̂.

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