What is the range of values of the random variable $Y = \frac{X - \min(X)}{\max(X)-\min(X)}$?

Question

Suppose $X$ is an arbitrary numeric random variable. Define the variable $Y$ as

$$Y=\frac{X-\min(X)}{\max(X)-\min(X)}.$$

Then what is the range of values of $Y$?

score 2 · Answer 1 · answered Jun 20 '13 at 13:15

2

If $X$ takes values over any finite (closed) interval, then the range of $Y$ is $[0,1]$.

answered Jun 20 '13 at 13:15

Ron Gordon

1

Just out of curiosity, why the downvote? I don't think I made any wildly inaccurate statement there. – Ron Gordon Jun 20 '13 at 13:20

1 Answers1