0

Suppose that $X$ is a given distribution. for an arbitrary increasing function $F_{Y}$ such that $\lim_{y \to \infty} F_{Y}(y)=1$ and $\lim_{y \to -\infty} F_{Y}(y)=0$, find the function $g$ such that if $Y=g(X)$, then $g$ is the CDF for $Y$.

My idea was to use the claim that is proved here, but I couldn't get what to do.

K.N
  • 397
  • 2
  • 13

1 Answers1

0

This is false. If $X=0$ then $g(X)=g(0)$ is a constant so you cannot choose $g$ so as to get a non-degenerate distribution.

Kavi Rama Murthy
  • 359,332