# Generates 5 random numbers from a uniform distribution [0, 1)
np.random.rand(5)
# Out: array([ 0.4071833 ,  0.069167  ,  0.69742877,  0.45354268,  0.7220556 ])

Using random.seed:

np.random.seed(0)
np.random.rand(5)
# Out: array([ 0.5488135 ,  0.71518937,  0.60276338,  0.54488318,  0.4236548 ])

By creating a random number generator object:

prng = np.random.RandomState(0)
prng.rand(5)
# Out: array([ 0.5488135 ,  0.71518937,  0.60276338,  0.54488318,  0.4236548 ])

# Creates a 5x5 random integer array ranging from 10 (inclusive) to 20 (inclusive)
np.random.randint(10, 20, (5, 5))

''' 
Out: array([[12, 14, 17, 16, 18],
            [18, 11, 16, 17, 17],
            [18, 11, 15, 19, 18],
            [19, 14, 13, 10, 13],
            [15, 10, 12, 13, 18]])
'''

letters = list('abcde')

Select three letters randomly (with replacement - same item can be chosen multiple times):

np.random.choice(letters, 3)
''' 
Out: array(['e', 'e', 'd'], 
      dtype='<U1')
'''

Sampling without replacement:

np.random.choice(letters, 3, replace=False)
''' 
Out: array(['a', 'c', 'd'], 
      dtype='<U1')
'''

Assign probability to each letter:

# Choses 'a' with 40% chance, 'b' with 30% and the remaining ones with 10% each
np.random.choice(letters, size=10, p=[0.4, 0.3, 0.1, 0.1, 0.1])

'''
Out: array(['a', 'b', 'e', 'b', 'a', 'b', 'b', 'c', 'a', 'b'],
  dtype='<U1')
'''

Draw samples from a normal (gaussian) distribution

# Generate 5 random numbers from a standard normal distribution
# (mean = 0, standard deviation = 1)
np.random.randn(5) 
# Out: array([-0.84423086,  0.70564081, -0.39878617, -0.82719653, -0.4157447 ])

# This result can also be achieved with the more general np.random.normal
np.random.normal(0, 1, 5)
# Out: array([-0.84423086,  0.70564081, -0.39878617, -0.82719653, -0.4157447 ])

# Specify the distribution's parameters
# Generate 5 random numbers drawn from a normal distribution with mean=70, std=10
np.random.normal(70, 10, 5)
# Out: array([ 72.06498837,  65.43118674,  59.40024236,  76.14957316,  84.29660766])

There are several additional distributions available in numpy.random, for example poisson, binomial and logistic

np.random.poisson(2.5, 5)  # 5 numbers, lambda=5
# Out: array([0, 2, 4, 3, 5])

np.random.binomial(4, 0.3, 5)  # 5 numbers, n=4, p=0.3
# Out: array([1, 0, 2, 1, 0])

np.random.logistic(2.3, 1.2, 5)  # 5 numbers, location=2.3, scale=1.2
# Out: array([ 1.23471936,  2.28598718, -0.81045893,  2.2474899 ,  4.15836878])