# Import the NumPy library
import numpy as np

def sliding_window_average(arr, window_size, sigma):
    x = np.linspace(-(window_size-1)/2, (window_size-1)/2, window_size)
    window = np.exp(-x**2 / (2*sigma**2))
    window /= window.sum()
    return np.convolve(arr, window, mode='valid')

# creating an array and calling function and printing results   
Z = np.arange(20)
print(sliding_window_average(Z, 3, 1))