Question

Using python, write a program to get the sample mean values with n=5 samples for 1000 experiments. Each sample has a normal distribution of ~N(0,1). This generates 1000 sample mean values.

Consider the sample mean value to be a random variable. Find its mean and variance.
(this should match part a)

Answer 1

Below is the python code to get the sample mean values with n=5 samples for 1000 experiments.

import numpy as np

samples = list()

for i in range(1000):

s = np.random.normal(0, 1, 5)

samples.append(s.mean())

np_samples = np.array(samples)

print(np_samples.mean())

print(np_samples.var())

I ran the code and got the result as shown in the image.

The sample mean should approach 0 and sample variance should approach 1/ 1000