## Poisson Binomial Distribution

Tags: #Math #Statistics### Equation

$$Pr(K = k) = \sum_{A \in F_{k}} \prod_{i \in A} p_{i} \prod_{j \in A_{c}} (1-p_{j})$$### Latex Code

Pr(K = k) = \sum_{A \in F_{k}} \prod_{i \in A} p_{i} \prod_{j \in A_{c}} (1-p_{j})

### Have Fun

Let's Vote for the Most Difficult Equation!

### Introduction

#### Equation

$$Pr(K = k) = \sum_{A \in F_{k}} \prod_{i \in A} p_{i} \prod_{j \in A_{c}} (1-p_{j})$$

#### Latex Code

Pr(K = k) = \sum_{A \in F_{k}} \prod_{i \in A} p_{i} \prod_{j \in A_{c}} (1-p_{j})

#### Explanation

Latex code for the Poisson Binomial Distribution. Poisson Binomial Distribution measures the probability of having k successful trials out of a total of n can be written as the sum. The success probability of each trial p1,p2,pn are not identical as the standard binomial distribution.

- The set of all subsets of k integers that can be selected from set {1,2,...,n} denotes: $$F_{k}$$
- The set of success trials : $$A$$
- The set of failed trials, which is also complement of set A: $$A^{c}$$

Reply