

In [1]:

    
import scipy as sp, numpy as np, pandas as pd
from matplotlib import pyplot as plt

1D Random walk

smaller title

$ \sum_1^100{1+i}$



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np.random.rand()









    Out[22]:





0.6076265125647292



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stepsize = 1
numsteps = 100
position = []
x = 0
for i in range(numsteps):
    number = np.random.rand()
    if number < 0.5:
        x = x - stepsize
    else:
        x = x + stepsize
    position = position + [x]
    # could have typed
    # position.append(x)



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plt.plot(position)









    Out[40]:





[<matplotlib.lines.Line2D at 0x1198b1ac8>]



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pos = np.array(position)



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np.average(pos)









    Out[34]:





8.322666666666667



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pos[-10]









    Out[35]:





51



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np.std(pos)









    Out[36]:





17.009053066594337



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df = pd.DataFrame(pos)



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df.plot()









    Out[43]:





<matplotlib.axes._subplots.AxesSubplot at 0x119669710>



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df.rolling(window=10).mean().plot()









    Out[44]:





<matplotlib.axes._subplots.AxesSubplot at 0x119669668>



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roll = df.rolling(window=10)



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m = roll.mean()



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m.plot()









    Out[47]:





<matplotlib.axes._subplots.AxesSubplot at 0x11af67cf8>



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