0.2 — Prerequisites for Applied Statistics#

Before diving into applied statistics, let’s review the essential mathematical and programming concepts you’ll need. Don’t worry if some concepts are new—we’ll cover them as needed throughout the course.

Mathematical Prerequisites#

Basic Probability#

While we focus on applied statistics (not theoretical probability), you should understand:

• Probability Basics: What probability means, basic probability rules
• Random Variables: Understanding that data comes from random processes
• Distributions: Familiarity with common distributions (normal, uniform)
• Expected Value: Understanding averages and means

Note: For a deep dive into probability theory, see our Quant Research course.

Basic Calculus#

You’ll need:

• Derivatives: Understanding rates of change
• Integrals: Understanding areas under curves (for probability densities)
• Basic Optimization: Finding minima/maxima (for maximum likelihood estimation)

Basic Algebra#

Essential skills:

• Linear Equations: Solving $y=mx+b$ type equations
• Logarithms: Understanding $\log$ and $\ln$ functions
• Exponentials: Understanding $e^x$ and related functions

Programming Prerequisites#

Python Basics#

You should be comfortable with:

• Variables and Data Types: Integers, floats, strings, lists
• Control Flow: If/else statements, loops
• Functions: Defining and calling functions
• Libraries: Importing and using libraries

NumPy Basics#

We’ll use NumPy extensively:

import numpy as np

# Arrays
arr = np.array([1, 2, 3, 4, 5])

# Basic operations
mean = np.mean(arr)
std = np.std(arr)

# Random numbers
random_data = np.random.normal(0, 1, size=100)

Pandas Basics#

We’ll use pandas for data manipulation:

import pandas as pd

# DataFrames
df = pd.DataFrame({'x': [1, 2, 3], 'y': [4, 5, 6]})

# Basic operations
mean_x = df['x'].mean()

Statistical Software#

We’ll primarily use:

• Python: NumPy, SciPy, pandas, scikit-learn
• Jupyter Notebooks: For interactive analysis
• Matplotlib/Seaborn: For visualization

What If You’re Missing Prerequisites?#

Don’t worry! This course is designed to be accessible:

1. We’ll Review: We’ll review key concepts as needed
2. Practical Focus: We focus on application, not deep theory
3. Code Examples: We provide working code you can learn from
4. Progressive Learning: Each chapter builds gradually

Next Steps#

In the next lesson, we’ll set up your Python environment with all the necessary libraries for statistical analysis.