4.9 Normal Distribution Theory Lesson 09
Comparison between a simple probability, binomial distribution, and normal distribution.
| Type | Quantity |
|---|---|
| Bernoulli | 1 |
| Binomial | 10 |
| Normal | 1000 |
Along this chapter I have seen the evolution from the simple probability (Bernoulli), to a Binomial, and finally a Normal distribution.
The difference is the size of the “sample”.
4.9.1 Equations
- Bernoulli
\[ P(HEADS) = P(HEADS)^n \tag{1}\]
- Binomial
\[P(n,k) = \frac{n!}{(n-k)!k!} p^k * (1-p)^{n-k} \tag{2}\]
- Normal (or Gaussian or Gauss or Laplace–Gauss) distribution
\[N(x;\mu,\sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}}\exp^{-\frac{1}{2} \frac{(x-\mu)^2}{\sigma^2}} \tag{3}\]
\(\mu\): mean; \(\sigma^2\): variance.
A work by AH Uyekita
anderson.uyekita[at]gmail.com