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How can I simplify the following probability equation based on cumulative distribution function of X:

P(X>a)>b

which P is the probability of X and X has a known probability distribution function and a & b are real positive numbers.

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    $\begingroup$ Do you the definition of a CDF? $\endgroup$ – user190080 Jul 31 '18 at 14:48
  • $\begingroup$ Back to the problem: Start with $X$ has cdf $F_X(X \le a) = 1 - P(X > a).$ You can get other, possibly useful, relationships from there. Not sure whether I'd call the 'simplifications'. $\endgroup$ – BruceET Aug 1 '18 at 4:40
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$$P(X>a)>b$$

$$-P(X>a)<-b$$ $$1-P(X>a)<1-b$$

$$P(X \le a)<1-b$$

$$F_X(a)<1-b$$

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