Can anyone please help me with this random variable question I've stumbled across.
Recall from calculus that a function $h$ is called non-decreasing if $x \le y$ implies $h(x) \le h(y)$, for every $x, y \in \mathop{\mathrm{dom}} h$.
Q1a) Let $X$ be a continuous random variable with probability density function $f$. Prove that the probability distribution function of $X$ is non-decreasing.
I'm assuming this means show $F(x) = \int_{-\infty}^x f(y)\,dy$, is a non-decreasing function of $x$ in $\mathbb R$.
Q1b) Show that $\lim_{x\to-\infty} F(x) = 0$ and $\lim_{x\to \infty} F(x) = 1$, and explain the probabilistic meaning of these facts.
Sorry about the layout i'm not used to using this site, hope it makes sense!