# -*- coding: utf-8 -*-
"""
Created on Thu Mar  8 12:12:10 2018

@author: megan
"""

# alternative way to import the random library:
#from random import *   # imports library random, and don't have to use the name when calling commands from it

import random as r
import pandas as pd
import matplotlib.pyplot as plt

# generates a randomly number for the uniform probability distribution on the interval [0,10]
# That is, generates a random real number between 0 and 10, with all numbers being equally likely
num = r.uniform(0,10)
print("Random number is",num)

# Comparision between how to generate a real random number between 0 and 10, 
# and how to generate a random integer between 0 and 10
num = r.uniform(0,10)
num_int = r.randint(0,10)
print("Random real number is",num)
print("Random integer is",num_int)


# To explore the uniform distribution, we will sample (generate) 100,000 numbers from it
# and plot them as a histogram.

# make an empty list to hold the numbers
num_list = []
# start your loop
for i in range(100000):
#  in the loop:  generate next number and add to list
    num = r.uniform(0,10)
    num_list.append(num)

# convert list into series
num_series = pd.Series(num_list)
# plot series as histogram
num_series.plot.hist(bins = 20)
plt.show()

# Estimates a probability density function from the data
num_series.plot.density()

# estimate probability a sampled number is between 2 and 4
# ~= # of numbers between 2 and 4/total # of numbers

# Create our condition variables
above2 = num_series >=2
below4 = num_series <= 4

# Apply the condition variables
btw2and4 = num_series[above2 & below4]

# compute the length of the series containing only numbers between 2 and 4
num_btw_2_and_4 = len(btw2and4)
# compute the lenght of the original series
total_num = len(num_series)
# estimate the probability the number is between 2 and 4 by dividing the number 
# of numbers in our sample between 2 and 4 with the total number of numbers in our sample
prob = num_btw_2_and_4/total_num
print("Estimated prob. between 2 and 4:",prob)