plot single vector with alpha

Hello,

I am trying to plot multiple intersecting lines from a given
array. In order to visualize the amount of crossing points I am
setting a certain alpha. However the crossings do not get darker as I
expected.

That is what I tried::

    import numpy as np
    import matplotlib.pyplot as plt

    x = np.random.randn(1000)
    y = np.random.randn(1000)

    plt.plot(x, y, alpha=.2, lw=1)
    plt.show()

What is the right way to do it?

Thanks & cheers,
Moritz