Formula and Diagram

Wikipedia

---

Exponential Distribution:

PDF

“Probability Density Function”

Formula:

$$f_x(t)=\{\begin{array}{cc}\lambda e^{-\lambda t}& \text{if}t\ge 0\\ 0& otherwise\end{array}$$

---

CDF

“Cumulative Distribution Function”

Formula:

$$F_x(t)=\{\begin{array}{cc}1-\lambda e^{-\lambda t}& \text{if}t\ge 0\\ 0& otherwise\end{array}$$

---

Notes:

• Notation: $\sim Exp(\frac{1}{\lambda })$
• Parameters: $\lambda >0$
• Support $x\in [0,\infty )$
• Mean: $\frac{1}{\lambda }$
• Median: $\frac{ln2}{\lambda }$
• Variance: $\frac{1}{{\lambda }^2}$
• The CDF is the differentiate of the PDF in respect to time:

$$f_x(t)=\frac{d{F}_x(t)}{dt}$$

---