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DeadxBunny
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Could someone tell me how to find the k in Chebyshev's inequality??
Parameter "k" is the number of standard deviations "σ" on either side of the mean "μ" for which a lower bound of the included distribution {fraction between (μ-kσ) and (μ+kσ)} is required {and given by this inequality to be (1 - 1/k^{2})}. See also Msg #4 at the following site (Form #1 in this Msg is most commonly used):DeadxBunny said:Could someone tell me how to find the k in Chebyshev's inequality??
Chebyshev's Inequality is a statistical theorem that provides an upper bound on the probability that a random variable will deviate from its mean by a certain number of standard deviations. It is a useful tool for understanding the spread of data in a distribution.
Chebyshev's Inequality is used to estimate the probability that a random variable will fall within a certain range of values. It is often used in combination with other statistical methods to analyze data and make predictions.
The formula for Chebyshev's Inequality is P(|X-μ| ≥ kσ) ≤ 1/k^2, where X is a random variable, μ is its mean, σ is its standard deviation, and k is the number of standard deviations from the mean.
Chebyshev's Inequality assumes that the data being analyzed is continuous and that the mean and standard deviation are known or can be estimated. It also assumes that the data is not highly skewed.
Chebyshev's Inequality provides a very conservative upper bound on the probability of deviation from the mean, meaning that it may overestimate the actual probability. It also does not provide any information about the shape of the distribution, such as whether it is skewed or symmetric.