# Lower bound on Tail Probabilities

Inequalities such as Markov's and Chebyshev’s provide upper bounds on tail probabilities. Are there similar inequalities that give lower bounds in the form $P(X \geq \alpha)>\theta$?

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## 1 Answer

Markov's inequality is also called the first moment method. What you want is the second moment method using bounds for the two first moments to derive the desired inequality :

http://en.wikipedia.org/wiki/Second_moment_method

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