This would not necessarily be true if were not an increasing function. Try taking the of both sides.
Niether would this.
Let be a random variable and denote its pdf
In general, let be an increasing function on the range of . Define . Show that
My question is how to incorporate the fact that g is an increasing function on the range of Y into my proof. I believe it belongs when I mess with the inverse, but I'm not sure how to say how I use that fact correctly.