Chebyshev's theorem

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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.
 

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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.
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.
 

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