Cumulative distribution function (cdf) question

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Prove or disprove: If X has a cdf F then P(F(X) <= a) <= a.  

Under what condition on F will you get P(F(X) <= a) = a?

Aug 25th, 2014

When we have uniform distribution between the limits 0 and 1

P(F(X)<=a) <=a

When a= 1

P (F(X)<=1) =1


Aug 25th, 2014

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Aug 25th, 2014
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Aug 25th, 2014
Oct 18th, 2017
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