1. ## chebyshev inequality

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

2. 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

3. 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

4. A symmetrical die is thrown 600 times.What is the lower bound of getting 80 to 120 sixes?

5. 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

6. 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 $\sqrt{npq}= \sqrt{100(1/6)(5/6)}= \frac{10}{6}\sqrt{5}= \frac{4\sqrt{5}}{3}$

20 is $\frac{20}{\frac{4\sqrt{5}}{3}}= \frac{15}{\sqrt{5}}= 3\sqrt{5}$ standard deviations.

7. That question needs to be done by using chebyshev inequality.

HENCE, divide 20 by $\sqrt{npq}$ and plug that into chebyshev's