# Constraints on Distribution Functions

Why does a distribution function $$F_X$$ have to be right continous ?
is'nt just making sure it is non-decreasing enough

## Answers and Replies

mathman
Science Advisor
In general, the continuity assumption of distribution functions at jumps is determined by convention. It could be right cont. or left cont. as long as it is used consistently. What you have is a non-zero prob. for the jump value. The main point is the precise definition of F(x) as a distribution function. You can have either of the following:
F(x)=P(X<x) - left continuous.
F(x)=P(X≤x) - right continuous.

Non-decreasing is required as well as the limit =1 at +∞.

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