# chebyshev inequality

• Jul 11th 2009, 10:29 PM
roshanhero
chebyshev inequality
In general what does the chebyshev inequality refers and how can I prove this theorem using integral signs?
• Jul 11th 2009, 10:41 PM
matheagle
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 AM
mr fantastic
Quote:

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

http://people.csail.mit.edu/ronitt/COURSE/S07/lec25.pdf

• Jul 12th 2009, 08:39 AM
roshanhero
A symmetrical die is thrown 600 times.What is the lower bound of getting 80 to 120 sixes?
• Jul 12th 2009, 01:30 PM
matheagle
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 PM
HallsofIvy
Quote:

Originally Posted by matheagle
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 igure out what 20 is in terms of the st. deviation
the variance is npq

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 PM
roshanhero
That question needs to be done by using chebyshev inequality.
• Jul 12th 2009, 05:30 PM
matheagle
HENCE, divide 20 by $\displaystyle \sqrt{npq}$ and plug that into chebyshev's