Is this the standard definition of cumulative distribution function? A cumulative probability function is usually defined as:

$$F_X(x)=P(X\leq x)$$

But is it ever also sometimes defined as follows?
$$F_X(x)=P(X&lt; x)$$

Is there a particular reason why the second one would be problematic, or incorrect, or less general?
The 2nd definition is less general, used by some Hungarian mathematicians.

Note if you use the 1st definition, you CDF is right-continuous; if you use the 2nd definition, your CDF is left-continuous and related definition and theorem will change a little bit.

Ok, just remember use the 1st one and that CDF always right-continuous.
The 2nd definition is less general, used by some Hungarian mathematicians.

Note if you use the 1st definition, you CDF is right-continuous; if you use the 2nd definition, your CDF is left-continuous and related definition and theorem will change a little bit.

Ok, just remember use the 1st one and that CDF always right-continuous.