Strengthen Markov’s inequality with conditional probability
by John from John D. Cook on (#6A3J4)
Markov's inequality is very general and hence very weak. Assume that X is a non-negative random variable, a > 0, and X has a finite expected value, Then Markov's inequality says that
In [1] the author gives two refinements of Markov's inequality which he calls Hansel and Gretel.
Hansel says
and Gretel says
[1] Joel E. Cohen. Markov's Inequality and Chebyshev's Inequality for Tail Probabilities: A Sharper Image. The American Statistician, Vol. 69, No. 1 (Feb 2015), pp. 5-7
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