import numpy as np
import scipy.stats as s

# normal distribution
# normal(mean, stdev, size)
heights = np.random.normal(188, 3, 10)
print heights

# binomial distribution
# binomial(n, p, size)
coinFlips = np.random.binomial(10, 0.5, 10)
print coinFlips

# normal density
x = np.linspace(-5, 5, num=10)
normalDensity = s.norm.pdf(x, 0, 1)
print np.around(normalDensity, decimals=2)

# binomial density
x = np.arange(0, 11, 1) # note that it's (0, 11, 1) instead of (0, 10, 1)
binomialDensity = s.binom.pmf(x, 10, 0.5)
print np.around(binomialDensity, decimals=2)

# 'sample' draws a random sample with and without replacement --> numpy.random.choice in numpy 1.7
heights = np.random.normal(188, 3, 10)

# with replacement
print 'random sampling with replacement:'
print np.random.choice(heights, size=10, replace=True, p=None)

# without replacement
print '\nrandom sampling without replacement'
print np.random.choice(heights, size=10, replace=False, p=None)

# sample according to a set of probability
probs = [0.4, 0.3, 0.2, 0.1, 0, 0, 0, 0, 0, 0]
print '\nrandom sampling with replacement according to a set of probability:'
print probs
print '\nsum of probabilities:'
print sum(probs)
print '\nsampled:'
print np.random.choice(heights, size=10, replace=True, p=probs)

# setting a seed
np.random.seed(12345)
print np.random.normal(0, 1, 5)
print '-------------------------------------------------------------'

np.random.seed(12345)
print np.random.normal(0, 1, 5)