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\[\begin{equation} E = m c^2 \tag{1.1} \end{equation}\]
Let’s start with a simple Formula:
\[\begin{equation} f\left(k\right) = \binom{n}{k} p^k\left(1-p\right)^{n-k} \tag{2.1} \end{equation}\]
The equation (2.1) is well known.
Another well known formula is the following:
Theorem 2.1 (Pythagorean theorem) For a right triangle, if \(c\) denotes the length of the hypotenuse and \(a\) and \(b\) denote the lengths of the other two sides, we have
\[\begin{equation} a^2 + b^2 = c^2 \tag{2.2} \end{equation}\]Which is this equation:
A normal paragraph.
plot(cars) # a scatterplot
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import numpy as np
import pandas as pd
x = np.random.randn(1000)
pd.Series(x).describe()
## count 1000.000000
## mean 0.033026
## std 0.990732
## min -2.569395
## 25% -0.644998
## 50% 0.033822
## 75% 0.691396
## max 3.274654
## dtype: float64
import seaborn
seaborn.set('paper')
import numpy as np
import matplotlib.pyplot as plt
xx = np.linspace(0, 10, 100)
yy = np.exp(0.1 * -xx) * np.sin(2 * xx)
plt.plot(xx, yy)
plt.grid(True)
plt.show()
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First check if you know about theorem 2.1 with the formula (2.2), that famous equation (1.1) and then look up what (2.1) is about!
… and don’t forget the figure 3.1!