Thread: probability inequality invovling function

Dear All.

I have read in somewhere that if f is non decreasing function then
, and even somewhere it is written
.

My question is this how this inequality is true, and which inequality is correct?

Can some explain in detail.

Regards.

Originally Posted by amb03

Dear All.

I have read in somewhere that if f is non decreasing function then
, and even somewhere it is written
.

My question is this how this inequality is true, and which inequality is correct?

Can some explain in detail.

Regards.

Neither is true. Consider f(x) = 0 for all values of x.

Do you mean f is strictly increasing?
In which case both are true since f(x) > f(y) iff x > y

It has more to do with set theory

If a<b and f is strictly increasing then f(a)<f(b)

If f is strictly increasing then the two sets are equal...

Thank for reply, but may you please check the following link, this inequality is stated here

http://www.cs.cmu.edu/afs/cs/academi...ribes/lec9.pdf

Regards

Originally Posted by matheagle

It has more to do with set theory

If a<b and f is strictly increasing then f(a)<f(b)

If f is strictly increasing then the two sets are equal...

Would you please explain me how is it possible?. I could not understand