ajey091

def mySqrt(self, x: int) -> int:
    high = x
    low = 0

    while low <= high:
        mid = low + (high-low)//2
        if mid * mid == x:
            return mid
        if mid * mid < x and (mid+1)*(mid+1) > x:
            return mid

ajey091

# estimate sample size via power analysis 
# We will use the statsmodels library to calculate the sample size.
from statsmodels.stats.power import TTestIndPower
# define parameters
effectsize = 0.1
alpha = 0.05
power = 0.8
# Statistical Power calculations for t-test for two independent sample
model = TTestIndPower()
samplesize = model.solve_power(effectsize, power=power, nobs1=None, ratio=1.0, alpha=alpha)

ajey091

import requests
from wordcloud import WordCloud
import urllib3
import re 

urllib3.disable_warnings(urllib3.exceptions.InsecureRequestWarning)

artist = input('Input artist name (default = Michael Jackson): ') or "Michael Jackson"
song = input('Input song name (default = Bad): ') or "Bad"
artist = artist.replace(' ','%2520')

ajey091

import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import norm

X_plot = np.linspace(130, 210, 1000)[:, np.newaxis]

mu1 = 178
mu2 = 163
sigma1 = 7.7
sigma2 = 7.3

ajey091

import matplotlib
import matplotlib.pyplot as plt
import numpy as np
import imageio
from scipy.stats import norm

def plot_for_offset(mu1, y_max):
    X_plot = np.linspace(-2, 12, 1000)[:, np.newaxis]
    
    mu2 = 5

ajey091

import numpy as np 
import matplotlib.pyplot as plt
import scipy.stats
from random import  uniform

p = scipy.stats.norm(0,1)

n = 50000
int_val = [0]*n
mean_val = [0]*n

ajey091

import numpy as np 
import matplotlib.pyplot as plt
import scipy.stats

f_x = scipy.stats.randint(1,7)

def g_x(x):
    return (7-x)/10/2.1

E_g = np.dot(np.linspace(1,6,6),g_x(np.linspace(1,6,6)))

ajey091

z = scipy.stats.norm.ppf(1-(1-0.95)/2)
print(f'Z-score for 95% confidence interval = {z:0.3f}')
moe = z*std_err
print (f'Margin of error={moe:.3f}')

ajey091

max_x_mean = np.mean(max_x)
std_err = np.std(max_x)/n**0.5
conf_int = np.percentile(max_x, [2.5,97.5])

print (f'mean of theta = {max_x_mean:.4f}')
print (f'Standard error of theta = {std_err:.4f}')
print (f'95% Confidence interval of theta = {conf_int}')

ajey091

max_x = []
for iter in range(1000):
    sample = rv.rvs(n)
    n1 = sum(sample == 0)
    n2 = n - n1
    x = np.linspace(0,1,100)
    L = x**n2 * (1-x)**n1
    curr_max_x = scipy.optimize.fmin(lambda x: -(x**n2 * (1-x)**n1), 0, disp=False)
    max_x.append(curr_max_x[0])