# Chebyshev's theorem

1. Nov 8, 2011

### risha

Chebyshev's theorem: If μ and σ are the mean and standard deviation of the random variable X, then for any positive constant k,the probability that X will take on a value within k standard deviations of the mean is at least [1-(1/k²)],that is,
P(|X-μ|<kσ) ≥ 1-1/k², σ≠0.
(i) given the chebyshev theorem,prove this theorenn using classical definition of variance.
(ii)Give an example of how this theorem can be used to calculate probability.

2. Nov 9, 2011

### SW VandeCarr

Are you asking us to answer this question for you? If this is a homework question, it should be posted in that forum with an attempt at a solution. In any case, we want to see your attempt at an answer.