Hey guys(adsbygoogle = window.adsbygoogle || []).push({});

I'd like a steer in the right direction with this problem.

I would like to show that

[tex]P\{x_1\leq X \leq x_2\}=F_{X}(x_2)-F_{X}(x_1^{-})\quad(1)[/tex]

Where:

[tex]X[/tex] is a random variable.

[tex]F_{X}(x) \equiv P\{X \leq x \} [/tex] is its cumulative distribution function.

My notes only give an example (using dice) to show that this is true.

Generally

[tex]P\{x_1 < X \leq x_2\}=F_{X}(x_2)-F_{X}(x_1)\quad(2)[/tex]

and

[tex]P\{X = x_2\}=F_{X}(x_2)-F_{X}(x_2^{-})\quad (3)[/tex]

the latter of which is easy to prove.

I've been trying to rewrite (1) in terms of (2) & (3) but have had no success so far.

Any ideas would be most welcomed

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proof with regards to cumulative distribution function

**Physics Forums | Science Articles, Homework Help, Discussion**