DES - Poisson Distribution

Wikipedia

---

Poisson Distribution:

PDF

“Probability Density Function”

Formula:

---

CDF

“Cumulative Distribution Function”

Formula:

Or: Or:

---

PMF

$$p_x(t)=\frac{{\lambda }^k{e}^{-\lambda }}{k!}$$

---

Notes:

• Notation: $\sim \mathrm{Pois}(\frac{1}{\lambda })$
• Parameters: $\lambda >0$ (rate)
• Support $k\in \mathbb{N}$ : Natural numbers starting from 0
• Mean: $\lambda$
• Median: $\approx \left[\lambda +\frac{1}{3}-0.02\frac{1}{\lambda }\right]$
• Variance: $\lambda$

---