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MIT6_042JS10_lec37_prob - Massachusetts Institute of...

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Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science May 7 Prof. Albert R. Meyer revised May 5, 2010, 847 minutes In-Class Problems Week 13, Fri. Problem 1. A herd of cows is stricken by an outbreak of cold cow disease . The disease lowers the normal body temperature of a cow, and a cow will die if its temperature goes below 90 degrees F. The disease epidemic is so intense that it lowered the average temperature of the herd to 85 degrees. Body temperatures as low as 70 degrees, but no lower , were actually found in the herd. (a) Prove that at most 3/4 of the cows could have survived. Hint: Let T be the temperature of a random cow. Make use of Markov’s bound. (b) Suppose there are 400 cows in the herd. Show that the bound of part ( a ) is best possible by giving an example set of temperatures for the cows so that the average herd temperature is 85, and with probability 3/4, a randomly chosen cow will have a high enough temperature to survive.
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