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UNIT V Probability Notes

Word Document · DOCX

Here's a summary of everything covered in the notes:

What's in the Notes

The document is structured into 7 sections with highlighted examples, formula boxes, shaded example panels, and quick-reference tables:

1. Probability – Core Concepts

  • Basic formula, independent vs dependent events
  • Addition Rule with die-roll example
  • Multiplication Rule with coloured-balls example
  • Conditional Probability with a student-subject example

2. Bayes' Theorem

  • Formula + all key terms (Prior, Posterior, Likelihood, Joint) in a table
  • Medical test example (shows the "base rate fallacy" – a 95% accurate test only gives 16% true-positive chance if disease is rare)
  • Factory defect example (which factory produced the defective item?)

3. Random Variables

  • Discrete vs Continuous comparison table with examples
  • PMF vs PDF explained simply

4. Probability Distributions

DistributionAdded Examples
BinomialDefective bulbs, email marketing, HR interviews
PoissonCall centre, traffic accidents, server error logs
ExponentialTime between calls, machine lifespan
NormalExam scores with Z-scores, bottled water quality control, student heights

5. Central Limit Theorem

  • Why it's powerful, all 4 conditions explained clearly
  • Examples: skewed salary data, dice simulation, supermarket wait times

6. Quick Reference Table

  • All 4 distributions side by side (type, use case, mean, variance, parameters)

7. Memory Aids

  • "When to use which?" decision guide
  • All key formulas in one place
  • 3 highlighted key-point reminders
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