12.1 Probability & Statistics Overview

Lesson Objective

You will learn:

How to describe a collection of data point as a distribution, and what some common distributions look like when plotted
How to describe a distribution using mean, variance, and standard deviation of a sequence of numbers
How to put a confidence metric around calculation of mean
Basic probability calculations and how to describe the likelihood of an event as a percentage

Let's Review Random Numbers

Random number generation in Python is a process of creating numbers that appear to be random and unpredictable, though they're actually generated through algorithms. These generators can be used in various applications like simulations, games, statistical sampling, and machine learning.

The three main ways we'll focus on for random number generation in Python are:

import random
- The pure Python way of generating random numbers
- Great for basic needs and straightforward randomization
import numpy as np
- Perfect for scientific computing and large datasets
- More powerful and faster for larger operations
import random, and import math
- Combines randomization with mathematical functions
- Useful when you need both random numbers and mathematical calculations in one

Examples:

Here are three simple examples that are easy to understand: Run, and modify to see how they work!

1.Using the "Random" library

Let's make a basic number picker - like rolling a digital dice!

a) Run the code and record the value.

b) Adjust the values from 1 to 20, to go to 1 to 500.

c) Run the code again and record the new value.

Coding Assistance: Click this link if you need help solving this problem.

2. Using the "Numpy" Library

Now let's create multiple random numbers all at once - rolling many dice together!

a) Run the code as is and record your output.

b) Alter the code to change the size=5 to a different number.

c) Run the new code and record your output.

Coding Assistance: Click this link if you need help solving this problem.

3. Using the combination of "Random" + "Math" libraries

Finally, let's use math with random numbers to plot points on a circle - like spinning a digital compass

a) Run the code as-is and record the point on the circle.

b) Change the radius to a larger value.

c) Run the new code and record the new point on the circle.

Coding Assistance: Click this link if you need help solving this problem.

SELF ASSESSMENT

Random Number generation is highly important in understanding probability and statistics. Let's check the foundational knowledge before continuing into statistical applications.

Probability & Statistics

Probability, Statistics, & Distribution.mp4

Practice Problem

Expected Output:

Try it yourself! Fill in the code to calculate the variance and standard deviation of the given dataset.

Coding Assistance: Click this link if you need help solving this problem.

Important Slides:

Sometimes, manually computing statistics like the standard deviation can be tedious. Thankfully, Python provides many pre-written functions that make these calculations quick and easy. Below is a list of important functions you can use when working with distributions. Feel free to refer back to this page as a reminder throughout this module!

SELF ASSESSMENT

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