# Is square root of a non-negative random variable also a random variable?

Let $X$ be a non-negative random variable and $Y=\sqrt{X}$

Is it true that $Y$ will also be a random variable?

Any hints please?

## 1 Answer

Hint. Note that $\sqrt{\cdot} \colon [0,\infty) \to [0,\infty)$ is monotone, hence measurable.