In teachingApps: Apps for Teaching Statistics, R Programming, and Shiny App Development

Properties of the Cumulative Distribution Function

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• The CDF relates the probability that the true (but unknown) value of the random variable $T$ is less than or equal to some observed value $t$

$$F(t)=Pr(T\le t), \quad t\in (0,\infty)$$

• The CDF is strictly positive

$$F(t) \ge 0, \forall t \in \mathbb{R}^{+}$$

• The CDF is non-decreasing

$$\begin{aligned}F(0)&=0\\\\ \displaystyle \lim_{t \to \infty} F(t)&=1\end{aligned}$$

• Alternate names for the CDF

  • The distribution function

  • The probability function

teachingApps documentation built on July 1, 2020, 5:58 p.m.