A Note on Chebyshev Inequality: To Explain or to Predict (Global Journal of Science Frontier Research, 2017)
The question is: What proportion of the total probability of a random varriable X lies within a certain interval of the mea ? What is the probability of being hit by a meteor greater in size than five times the standard deviation above the mean? Because it can be applied to completely arbitrary distributions(unknown except for mean and variables), the inequality generally gives a poor bound compared to what might be deduced if more aspects are known about the distribution involved.
Keywords: eucladian norm; monotonic function; jensen inequality