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, 10:29 PMroshanherochebyshev inequality
In general what does the chebyshev inequality refers and how can I prove this theorem using integral signs?

- Jul 11th 2009, 10:41 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, 04:34 AMmr fantastic
- Jul 12th 2009, 08:39 AMroshanhero
A symmetrical die is thrown 600 times.What is the lower bound of getting 80 to 120 sixes?

- Jul 12th 2009, 01:30 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, 03:12 PMHallsofIvy
But the "standard deviation" is

**defined**as the square root of the variance. Since the variance is "npq", the standard deviation is $\displaystyle \sqrt{npq}= \sqrt{100(1/6)(5/6)}= \frac{10}{6}\sqrt{5}= \frac{4\sqrt{5}}{3}$

20 is $\displaystyle \frac{20}{\frac{4\sqrt{5}}{3}}= \frac{15}{\sqrt{5}}= 3\sqrt{5}$ standard deviations. - Jul 12th 2009, 03:58 PMroshanhero
That question needs to be done by using chebyshev inequality.

- Jul 12th 2009, 05:30 PMmatheagle
we answered that

20 is how many st deviations...

HENCE, divide 20 by $\displaystyle \sqrt{npq}$ 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.