Probability & Statistics

Unit 1 – Foundations of Probability (8 hrs)

1. “Probability as Weather Forecasting – Predicting the Unpredictable” (Basic Notions of Probability, Events, Set Operations)

2. “Conditional Probability as Knowing You’re Already in the Elevator” (Conditional Probability & Independence)

3. “Bayes’ Theorem: Detective Work with Clues and Updates” (Applications of Bayes’ Theorem)

4. “Random Variables: Dice Rolls vs Thermometer Readings” (Discrete & Continuous Random Variables)

5. “CDF & PDF: Maps of Probability – From Cumulative Journeys to Instant Snapshots” (CDF, PMF, PDF)

6. “Expectation & Moments: The Center of Gravity in Data” (Mathematical Expectation & Moments)

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Unit 2 – Engineering Applications of Probability Distributions (8 hrs)

7. “Joint & Marginal Distributions: Overlapping Circles in a Probability Venn Diagram” (Joint & Marginal Distributions)

8. “Bernoulli Trials as Yes-or-No Coin Tosses” (Bernoulli)

9. “Binomial Distributions: Counting Successes in a Fixed Number of Tries” (Binomial)

10. “Geometric Distributions: Waiting for the First Success Like Fishing” (Geometric)

11. “Poisson Distribution: Counting Rare Events Like Shooting Stars” (Poisson)

12. “Uniform Distribution: Rolling a Perfectly Fair Die” (Uniform)

13. “Exponential Distribution: Time Between Bus Arrivals” (Exponential)

14. “Normal Distribution: The Bell Curve Behind Human Heights” (Normal)

15. “Central Limit Theorem: Why Many Things in Life Turn Bell-Shaped” (CLT)

16. “Law of Large Numbers: More Trials, More Truth” (LLN)

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Unit 3 – Descriptive Statistics and Regression Analysis (8 hrs)

17. “Measures of Central Tendency: The Average Taste Test” (Mean, Median, Mode)

18. “Measures of Variability: How Different Are the Cookies in the Batch?” (Variance, Standard Deviation)

19. “Histograms & Scatter Plots: The Photography of Data” (Visualization Techniques)

20. “Correlation vs Covariance: Dancing Together or Just Moving in the Same Direction” (Correlation & Covariance)

21. “Linear Regression: Drawing the Best-Fit Line in a Sea of Dots” (Linear Regression)

22. “Least Squares Method: Minimizing the Wobble in Your Prediction Line” (Least Squares)

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Unit 4 – Inferential Statistics for Engineers (8 hrs)

23. “Statistical Inference: Making Big Claims from Small Samples” (Intro to Statistical Inference)

24. “Sampling Distributions: Repeatedly Scooping Soup to Check the Flavor” (Sampling Distributions)

25. “Point & Confidence Intervals: Pinpointing the Target with a Margin of Error” (Estimation Techniques)

26. “Hypothesis Testing as a Court Trial – Evidence, Doubt, and Verdicts” (Hypothesis Testing Basics)

27. “Z-Test, T-Test, and Friends: Different Tools for Different Data Crimes” (Parametric Tests)

28. “Non-Parametric Tests: When You Can’t Assume the Bell Curve” (Non-Parametric Tests)

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