How do I prove this? *Let F be a distribution function. Show that F is right continuous.

Question

order statistics is a general topic that captures the question 

Answer 1

Every cumulative distribution function is non-decreasing and right continuous.

 

There are no discontinuities from the right 

 

That is limit F(x)  X--->c+ exists 

 

One way to prove it would be to argue that the derivative exists as the limit approaches from the right.

 

It is differentiable because the derivative of the density function is the pdf.

Differentiability guarantees continuity