Illustration with Python Central Limit Theorem | expected value and standard deviation of sample means

muandSigmaSampleMean.py

## expect value of sample
import numpy as np

# use last sampling
from diffSampleSize import meansample
# mean and standard deviation from population
shape, scale = 2., 2.  # mean=4, std=2*sqrt(2)
sample = meansample[5]
# expected value of sample equal to expect value of population
print("expected value of sample:", np.mean(sample))
print("expected value of population:", shape*scale)
# standard deviation of sample equl to standard deviation of population divided by squre root of n
print("standard deviation of sample:", np.std(sample))
print("standard deviation of population:", scale*np.sqrt(shape))
print("standard deviation of population divided by squre root of sample size:", scale*np.sqrt(shape)/np.sqrt(1000))