Gaussian pdf distribution

For some details, check here. As for the product of two functions, that's easy as you can see. Intuition 1 Multiplying random variables : Suppose kids save money Y for X days before giving up. X is random iid normally distributed variable from 0 days to 10 days.

Average kid saves for 5 days. Average kid saves 0. What's the distribution? Now are the savings of a kid normally distributed? We know the mean, median, mode of a normal distribution are same as it is symmetric with a standard deviation.

The max savings are 5 and the min is 0. The median of 5 and 0 is 2. The mean and median don't match so the product is not normally distributed. The distribution is shifted to the left from the 2. The probability that a kid saved 1 is higher than the probability that he saved 4.

The multiplying is just a bunch of algebra and the resulting function also fits the form factor of a Gaussian. The proof for that is given in your link. It means if you have populations of kids there will be a Gaussian representing their savings with some average savings from each sub population. Basically, a mixture of gaussians is a gaussian. Maybe given distributions of daily savings and total savings you want to establish the distribution of how long the kids tend to save.

Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Asked 6 years, 11 months ago. Active 8 months ago. Viewed 96k times. Lyndon White Lyndon White 1, 1 1 gold badge 11 11 silver badges 22 22 bronze badges.

Add a comment. Active Oldest Votes. Gabriel Barello Gabriel Barello 1 1 silver badge 2 2 bronze badges. Albert Chen Albert Chen 2 2 silver badges 8 8 bronze badges. Aditya Mittal Aditya Mittal 4 4 bronze badges. The other answer by Lyndon has the reverse problem. I'd hate to be in the OPs position trying to determine which of your answers is accepted. How to plot Gaussian distribution in Python We have libraries like Numpy, scipy, and matplotlib to help us plot an ideal normal curve.

Python3 import numpy as np import scipy as sp from scipy import stats import matplotlib. Skip to content. Change Language. Related Articles.

Table of Contents. Improve Article. Save Article. Like Article. What is normal or Guassian distribution? Define the Gaussian function. Recast xdata and ydata into numpy arrays so we can use their handy features. Let's create a function to model and create data. Plot out the current state of the data and model. Attention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.