Why Probability Matters
Probability is the mathematics of uncertainty. In data science, we use probability to quantify uncertainty in predictions, make inferences about populations from samples, build probabilistic models, and test hypotheses.
Fundamental Concepts
Sample Space and Events
Basic Probability Rules
Probability Distributions
Discrete Distributions
Continuous Distributions
PDF vs CDF
Bayes' Theorem
Intuitive Understanding
Example: Medical Testing
Naive Bayes Classification
Central Limit Theorem (CLT)
Practical Example: A/B Testing with Bayesian Analysis
Key Takeaways
Practice Exercise
- Calculate the probability of getting exactly 3 heads in 5 fair coin flips using the Binomial distribution
- Apply Bayes' Theorem to a drug testing scenario: 2% prevalence, 95% sensitivity, 90% specificity
- Demonstrate CLT by sampling from an exponential distribution with n = 2, 10, 30, 100
- Build a Bayesian A/B testing framework that computes P(B > A) for different sample sizes
- For a Poisson process with λ = 3 events/hour, compute the probability of observing 0-5+ events
- Compare the PDF and CDF of the normal distribution visually
- Verify that P(Μ - σ ≤ X ≤ Μ + σ) ≈ 0.6827 for a standard normal