import numpy
import scipy.stats as stats
from datascience import *
%matplotlib inline
import matplotlib.pyplot as plots
plots.style.use('fivethirtyeight')
import numpy as np
import scipy.stats as stats


def biasdemo1():
    
    np.random.seed(15)
    Population = np.random.normal(15000,500,100000)
    PopSigma = np.round(np.std(Population),0)

    Biased = make_array()
    Unbiased=make_array()

    reps = 20

    for i in np.arange(reps):
        Sample = np.random.choice(Population, 3)
        Biased = np.append(Biased, np.std(Sample))
        Unbiased = np.append(Unbiased, stats.tstd(Sample))

    biasedmean = np.round(np.mean(Biased),0)
    unbiasedmean = np.round(np.mean(Unbiased),0)
    
    plots.figure(figsize=(12,6))
    plots.suptitle("Biased = Bad, Unbiased = Good")

    plots.subplot(1,2,1)
    plots.hist(Biased)
    plots.scatter(PopSigma, -3, marker="^", zorder=5, s=80, color='green')
    plots.scatter(np.mean(Biased),-3, marker = "s", zorder=5, s=80, color='red')
    plots.title("Biased Estimator of Sigma")
    plots.text(710, 0.1*reps, f"Estimator = {biasedmean}", color='red')
    plots.text(710, 0.085*reps,f"True Value = {PopSigma}", color='green');

    plots.subplot(1,2,2)
    plots.hist(Unbiased)
    plots.scatter(PopSigma, -3, marker="^", zorder=5, s=80, color='green')
    plots.scatter(np.mean(Unbiased),-3, marker = "s", zorder=5, s=80, color='red')
    plots.title("Unbiased Estimator of Sigma")
    plots.text(710,  0.1*reps, f"Estimator = {unbiasedmean}", color='red')
    plots.text(710,  0.085*reps,f"True Value = {PopSigma}", color='green');