From d5499f54b318fff4a7d14a7044bc0ee03acde6e0 Mon Sep 17 00:00:00 2001 From: Lodewijk Nauta Date: Fri, 13 Jan 2017 12:05:40 +0100 Subject: [PATCH] expanded formula for poisson distribution to include lambda --- Chapter1_Introduction/Ch1_Introduction_PyMC2.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Chapter1_Introduction/Ch1_Introduction_PyMC2.ipynb b/Chapter1_Introduction/Ch1_Introduction_PyMC2.ipynb index 87c3e72e..4e1bfedc 100644 --- a/Chapter1_Introduction/Ch1_Introduction_PyMC2.ipynb +++ b/Chapter1_Introduction/Ch1_Introduction_PyMC2.ipynb @@ -404,7 +404,7 @@ "### Discrete Case\n", "If $Z$ is discrete, then its distribution is called a *probability mass function*, which measures the probability $Z$ takes on the value $k$, denoted $P(Z=k)$. Note that the probability mass function completely describes the random variable $Z$, that is, if we know the mass function, we know how $Z$ should behave. There are popular probability mass functions that consistently appear: we will introduce them as needed, but let's introduce the first very useful probability mass function. We say $Z$ is *Poisson*-distributed if:\n", "\n", - "$$P(Z = k) =\\frac{ \\lambda^k e^{-\\lambda} }{k!}, \\; \\; k=0,1,2, \\dots $$\n", + "$$P(Z = k) =\\frac{ \\lambda^k e^{-\\lambda} }{k!}, \\; \\; k=0,1,2, \\dots, \\; \\; \\lambda \\in \\mathbb{R}_{>0} $$\n", "\n", "$\\lambda$ is called a parameter of the distribution, and it controls the distribution's shape. For the Poisson distribution, $\\lambda$ can be any positive number. By increasing $\\lambda$, we add more probability to larger values, and conversely by decreasing $\\lambda$ we add more probability to smaller values. One can describe $\\lambda$ as the *intensity* of the Poisson distribution. \n", "\n",