Here: loc = 50 represents the mean. scale = 10 represents the standard deviation.

🔹 17. Common Mistakes

❌ Confusing PMF and PDF → Remember: PMF → Discrete, PDF → Continuous

❌ Thinking PDF value is probability → For a continuous distribution, the PDF value at a point is a density, not the probability of that exact value. Probability comes from the area over an interval.

❌ Forgetting that CDF is cumulative → CDF always represents: P(X ≤ x)

🎯 Practice Questions

1. What is the difference between a discrete and continuous random variable?

2. What is PMF used for?

3. What does a PDF represent?

4. What does CDF calculate?

5. Name three probability distributions commonly used in Data Science.

🎯 Key Takeaways

✅ Probability distributions describe how probabilities are distributed across possible outcomes.

✅ Discrete variables have countable outcomes.

✅ Continuous variables can take infinitely many values within a range.

✅ PMF is used for discrete random variables.

✅ PDF is used for continuous random variables.

✅ CDF gives the cumulative probability up to a particular value.

✅ Normal, Binomial, and Poisson distributions are important distributions for Data Scientists.

Understanding probability distributions gives you the foundation needed for statistical inference, hypothesis testing, machine learning, and advanced Data Science.

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