Bernoulli distributions

Let's begin with a simple distribution: one that has a binary outcome, and is very much like tossing a (fair) coin.

This distribution represents a single event that takes the value 1 (let's call this heads) with a probability of p, and 0 (lets call this tails), with probability 1-p.

In order to visualize this, let's generate a large number of events of a Bernoulli distribution using np and graph the tendency of this distribution, with the following only two possible outcomes:

    plt.figure() 
    distro = np.random.binomial(1, .6, 10000)/0.5 
    plt.hist(distro, 2 , normed=1) 

The following graph shows the binomial distribution, through an histogram, showing the complementary nature of the outcomes' probabilities:

So, here we see the very clear tendency of the complementing probabilities of the possible outcomes. Now let's complement the model with a larger number of possible outcomes. When their number is greater than 2, we are talking about a multinomial distribution:

    plt.figure()
    distro = np.random.binomial(100, .6, 10000)/0.01 
    plt.hist(distro, 100 , normed=1) 
    plt.show() 

Take a look at the following graph: