Question

Write the python code that generates a normal sample with given μ and σ, and the code that calculates m (sample mean) and s (sample standard deviation) from the sample.

Answer 1

Code for generate a normal sample:

import numpy as np

def main():
    #get input for mean
    mean = int(input("Please enter mean: "))
    #get input for standard deviation
    stdev = int(input("Please enter standard deviation: "))
    #generate samples with mean and standard deviation
    samples = generateSamples(mean, stdev, 100000)

    print('Normal sample: ', samples)
    print('Mean:', samples.mean())
    print('Standard deviation:', samples.std())
    return

def generateSamples(mean, stdev, n=1):
    # Calculate mu and sigma of normal distribution
    meanSqr = mean ** 2
    phi = (stdev ** 2 + meanSqr) ** 0.5
    sigma = (np.log(phi ** 2 / meanSqr)) ** 0.5
    mu = np.log(meanSqr / phi)
    # Generate normal population
    normal_samples = np.random.lognormal(mu, sigma , n)
    # Convert single sample (if n=1) to a float, otherwise leave as array
    normal_samples = normal_samples[0] if len(normal_samples) == 1 else normal_samples
    return normal_samples

#Call method
main()

Code Screenshot:

Sample output: