Chebyshev's Inequality

maryammalik · #1 Monday, January 31, 2011

I would be really grateful if anyone help me sort out the following question of 2001 CSS paper.

> State Chebyshev's inequality. Estimate the demand interval such that the probability is at leat 8/9 that the demand will remain or lie in that interval.

Thanks in advance.

Bilal Salim · #2 Wednesday, February 02, 2011

Chebyshev’s inequality
A theorem that characterizes the dispersion of data away from its mean

Chebyshev’s inequality puts an upper bound on the probability that an observation should be far from its mean. It requires only two minimal conditions: (1) that the underlying distribution have a mean and (2) that the average size of the deviations away from this mean (as gauged by the standard deviation) not be infinite.
The probability that an observation will be more than k standard deviations from the mean is at most 1/k2.(k square)

Bilal Salim · #3 Wednesday, February 02, 2011

the interval is mean(+-) 3*S.D.
1/9=1/k2 thus k=3