I have the following depictions in my lecture notes, which I fail to understand. It talks about functions of random variables and distinguishes between the two cases, when the function of a random variable $g(X)$ is strictly monotonic. $Y,X$ are random variables and $Y=g(X)$:
I do not understand why $P(X\leq x)=P(Y \leq y)$
Same question. Sorry about the quality.