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4.1B – Probability Distribution

4.1B – Probability Distribution. MEAN of discrete random variable: µ = Σ xP (x) EACH x is multiplied by its probability and the products are added. µ = EXPECTED VALUE of discrete random variables. Example: Find the Mean. Example: Find the Mean. Example: Find the Mean.

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4.1B – Probability Distribution

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  1. 4.1B – Probability Distribution • MEAN of discrete random variable: µ = ΣxP(x) • EACH x is multiplied by its probability and the products are added. • µ = EXPECTED VALUE of discrete random variables

  2. Example: Find the Mean

  3. Example: Find the Mean

  4. Example: Find the Mean

  5. Example: Find the Mean

  6. Example: Find the Mean

  7. Example: Find the Mean

  8. Example: Find the Mean

  9. Example: Find the Mean

  10. Example: Find the Mean

  11. Example: Find the Mean

  12. Example: Find the Mean

  13. Example: Find the EXPECTED VALUE of your gain. • 1500 tickets are sold for $2 each for 4 prizes of $500, $250, $150, and $75. You buy 1 ticket. What is the expected value of your gain?

  14. Example: Find the EXPECTED VALUE of your gain. • 1500 tickets are sold for $2 each for 4 prizes of $500, $250, $150, and $75. You buy 1 ticket. What is the expected value of your gain?

  15. Example: Find the EXPECTED VALUE of your gain. • 1500 tickets are sold for $2 each for 4 prizes of $500, $250, $150, and $75. You buy 1 ticket. What is the expected value of your gain?

  16. Example: Find the EXPECTED VALUE of your gain. • 1500 tickets are sold for $2 each for 4 prizes of $500, $250, $150, and $75. You buy 1 ticket. What is the expected value of your gain?

  17. Example: Find the EXPECTED VALUE of your gain. • 1500 tickets are sold for $2 each for 4 prizes of $500, $250, $150, and $75. You buy 1 ticket. What is the expected value of your gain?

  18. Example: Find the EXPECTED VALUE of your gain. • 1500 tickets are sold for $2 each for 4 prizes of $500, $250, $150, and $75. You buy 1 ticket. What is the expected value of your gain?

  19. Example: Find the EXPECTED VALUE of your gain. • 1500 tickets are sold for $2 each for 4 prizes of $500, $250, $150, and $75. You buy 1 ticket. What is the expected value of your gain?

  20. Example: Find the EXPECTED VALUE of your gain. • 1500 tickets are sold for $2 each for 4 prizes of $500, $250, $150, and $75. You buy 1 ticket. What is the expected value of your gain?

  21. Example: Find the EXPECTED VALUE of your gain. • 1500 tickets are sold for $2 each for 4 prizes of $500, $250, $150, and $75. You buy 1 ticket. What is the expected value of your gain?

  22. Example: Find the EXPECTED VALUE of your gain. • 1500 tickets are sold for $2 each for 4 prizes of $500, $250, $150, and $75. You buy 1 ticket. What is the expected value of your gain?

  23. Example: Find the EXPECTED VALUE of your gain. • 1500 tickets are sold for $2 each for 4 prizes of $500, $250, $150, and $75. You buy 1 ticket. What is the expected value of your gain?

  24. Example: Find the EXPECTED VALUE of your gain. • 1500 tickets are sold for $2 each for 4 prizes of $500, $250, $150, and $75. You buy 1 ticket. What is the expected value of your gain?

  25. Standard Deviation • VARIANCE of discrete random variable σ² = Σ(x-µ)²P(x) OR σ² = [Σx²P(x)] - µ² • STANDARD DEVIATION of discrete random variable σ = √σ²

  26. Example: Find Variance & Standard Deviation σ = √σ²

  27. Example: Find Variance & Standard Deviation σ = √σ²

  28. Example: Find Variance & Standard Deviation σ = √σ²

  29. Example: Find Variance & Standard Deviation σ = √σ²

  30. Example: Find Variance & Standard Deviation σ = √σ²

  31. Example: Find Variance & Standard Deviation σ = √σ²

  32. Example: Find Variance & Standard Deviation σ = √σ²

  33. Example: Find Variance & Standard Deviation σ = √σ²

  34. Example: Find Variance & Standard Deviation σ = √σ²

  35. Example: Find Variance & Standard Deviation σ = √σ²

  36. Example: Find Variance & Standard Deviation σ = √σ²

  37. Example: Find Variance & Standard Deviation σ = √σ²

  38. Example: Find Variance & Standard Deviation σ = √σ²

  39. Example: Find Variance & Standard Deviation σ = √σ²

  40. Example: Find Variance & Standard Deviation σ = √σ²

  41. Example: Find Variance & Standard Deviation σ = √σ²

  42. Example: Find Variance & Standard Deviation σ = √σ²

  43. Example: Find Variance & Standard Deviation σ = √σ² = √1.616 = 1.27

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