## Geometric Distribution

Tags: #Math #Statistics### Equation

$$Pr(X=k) = (1-p)^{k-1}q, \\ f(x)=(1-p)^{k-1}q, \\ F(x)=1 - (1-p)^{[x]}$$### Latex Code

Pr(X=k) = (1-p)^{k-1}q, \\ f(x)=(1-p)^{k-1}q, \\ F(x)=1 - (1-p)^{[x]}

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### Introduction

#### Equation

$$Pr(X=k) = (1-p)^{k-1}q$$ $$f(x)=(1-p)^{k-1}q$$ $$F(x)=1 - (1-p)^{[x]}$$

#### Latex Code

Pr(X=k) = (1-p)^{k-1}q, \\ f(x)=(1-p)^{k-1}q, \\ F(x)=1 - (1-p)^{[x]}

#### Explanation

Latex code for the Geometric Distribution.

- Probability parameter p means the success probability of each trial: $$p$$
- The number of total trials until the first successful trial k: $$k$$
- PDF for Geometric Distribution: $$f(x)=(1-p)^{k-1}q$$
- CDF for Geometric Distribution: $$F(x)=1 - (1-p)^{[x]}$$

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