In general what does the chebyshev inequality refers and how can I prove this theorem using integral signs?

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- Jul 11th 2009, 11:29 PMroshanherochebyshev inequality
In general what does the chebyshev inequality refers and how can I prove this theorem using integral signs?

- Jul 11th 2009, 11:41 PMmatheagle
as usual I don't understand your questions

what is 'integral signs'?

The proof consists of splitting the integral into two pieces and throwing away one

and using an inequality on the other

http://en.wikipedia.org/wiki/Chebyshev's_inequality - Jul 12th 2009, 05:34 AMmr fantastic
- Jul 12th 2009, 09:39 AMroshanhero
A symmetrical die is thrown 600 times.What is the lower bound of getting 80 to 120 sixes?

- Jul 12th 2009, 02:30 PMmatheagle
that's a binomial problem that can be fairly approximated with the normal ditsribution via the central limit theorem

n=100, p=1/6 hence the mean is 100

you need to figure out what 20 is in terms of the st. deviation

the variance is npq - Jul 12th 2009, 04:12 PMHallsofIvy
- Jul 12th 2009, 04:58 PMroshanhero
That question needs to be done by using chebyshev inequality.

- Jul 12th 2009, 06:30 PMmatheagle
we answered that

20 is how many st deviations...

HENCE, divide 20 by and plug that into chebyshev's

AND lower bound on what?

we assume you mean probabilities here.

solve for k and plug into the inequality on either of those links.