MATH 328 Week 7 Discussion

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 Week 7 Forum: Limit Theorems and Additional Topics / Chebyshev’s Inequality, the Markov Inequality, and the Central Limit Theorem

Chebyshev’s Inequality, the Markov Inequality, and the Central Limit Theorem

Chapters 8 and 9 discuss a number of topics which have widespread applicability to real world applications. The Central Limit Theorem for example is fundamental to all sampling done for all research studies – without it, large-scale research studies would lose much of their utility. Likewise Chebyshev’s Inequality (also known as Chebyshev’s Theorem) is useful when dealing with continuous distributions which are not normal in shape; likewise so is Markov’s Inequality.

For this final week of new topics (remember that next week is the final exam, so we will not be introducing any new material) let’s discuss some typical real world situations where you find these three relationships being applied. Pick one such situation and describe it in some detail. What was the most interesting – or surprising - thing you learned about how the theorem is being put to use?

Please try, if possible, to pick a situation to discuss that nobody else has explored in depth yet. Put the application you chose to explore in depth in the subject line heading of your initial post (for example, “Chebyshev’s Inequality applied to stock market pricing”).

Our textbook in chapter 7 contains a number of specific examples and homework problems to give you ideas. You can also search online to find real world examples of these three relationships. Some good websites to start out with are listed below (but there are many, many others online, so please don’t limit yourself to these):

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&ved=0CEkQFjAE&url=http%3A%2F%2Fwww.fordham.edu%2Feconomics%2Fvinod%2Fsampl-dis.doc&ei=Kl5kUr_MMarwyAHnm4HwAg&usg=AFQjCNHp2DrHoWl8Y2E6v0m4AeUXobC2Fg&sig2=EsbP4jpH8XQkPdjSHFa0Eg&bvm=bv.54934254,d.aWc

and

http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Central_limit_theorem.html

and

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=27&cad=rja&ved=0CE8QFjAGOBQ&url=http%3A%2F%2Fwww.dartmouth.edu%2F~chance%2Fteaching_aids%2Fbooks_articles%2Fprobability_book%2FChapter9.pdf&ei=5HBkUv_kEoGmyQGK44GYDw&usg=AFQjCNGGqh7LtL8S5jrGTXLRIXTa70iTpg&sig2=cnNJaoJoJSQQqMBkjqj9eA&bvm=bv.54934254,d.aWc

Be sure to include the source(s) you use in your post.

Instructions: Your initial post should be at least 250 words. In addition, please respond to at least 2 other students. Your responses should help develop discussion around the topic/feedback that your classmate presented. Responses to students should be a minimum of 100 words each.