Mathematics
Cumulative distribution function (cdf) question

Question Description

I’m studying for my Statistics class and need an explanation.

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?

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When we have uniform distribution between the limits 0 and 1

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

When a= 1

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

UIUC
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