- Thread starter
- #1

- Thread starter bl00d
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- Thread starter
- #1

- Feb 13, 2012

- 1,704

If X is a continous r.v. then $F_{X} (x) = P \{ X < x\}$ is continous. Now if $y=g(x)$ is continous then $x=g^{-1} (y)$ is also continous and the same is for...If X is a continuous random variable and g is a continuous function

defined on X (Ω), then Y = g(X ) is a continuous random variable.

Prove or disprove it.

$$F_{Y} (y) = P \{g(X) < y\} = P \{X < g^{-1} (Y)\} = F_{X} (g^{-1} (y))$$

Kind regards

$\chi$ $\sigma$