## probablility density functions
\begin{align}
\mbox{Gaussian} \\
\ g(y, \mu, \sigma) = \frac{1}{\sigma \sqrt{2 \pi}}  \exp{\frac{-(y - \mu)^2}{2 \sigma^2}} \\
\end{align}
## adaptable parameters
\begin{align}
\Delta \mu = \alpha_{\mu} (r - b{\mu}) \frac{y - \mu}{\sigma^2} \\
\\
\Delta \sigma = \alpha_{\sigma} (r - b{\sigma}) \frac{(y - \mu)^2 - \sigma^2}{\sigma^3} \\
\end{align}


```python
%matplotlib notebook
import matplotlib.pyplot as plt
import numpy as np

def g(y,u,s):
    c = 1 / (np.sqrt(2*np.pi) * s)
    return c * np.exp((-(y-u)**2)/(2*s**2))
```


```python
n_points = 1000
u = 6
s = 1
x = np.linspace(3, 9, n_points)
y = g(x,u,s)
plt.plot(x, y)
```


    <IPython.core.display.Javascript object>









    [<matplotlib.lines.Line2D at 0x114065e10>]




```python
s - 0.9
s_hi = u + s
s_lo = u - s
print('number >= %0.2f'%cutoff, sum(np.random.normal(u,s, n_points) <= s_hi))
print('number >= %0.2f'%cutoff, sum(np.random.normal(u,s, n_points) <= s_lo))
```

    number >= 7.00 805
    number >= 7.00 163



```python



```


```python

```

e03e4e597b9b68103299c4355fed36ee93c892cf
ipynb
Jupyter Notebook
development_notebooks/probablilty_density.ipynb
dlanier/FlyingMachineFractal
3889bfb8b8005717de83954d4a705154e908273b
MIT
2017-03-27T19:50:37.000Z
2021-07-15T03:23:03.000Z
development_notebooks/probablilty_density.ipynb
dlanier/FlyingMachineFractal
3889bfb8b8005717de83954d4a705154e908273b
MIT
development_notebooks/probablilty_density.ipynb
dlanier/FlyingMachineFractal
3889bfb8b8005717de83954d4a705154e908273b
MIT
2017-03-27T19:50:54.000Z
2017-03-27T19:50:54.000Z
Qwen/Qwen-72B
1. YES
2. YES