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Islamic University of Gaza Statistics and Probability for Engineers (ENGC 6310)

Islamic University of Gaza Statistics and Probability for Engineers (ENGC 6310). Lecture 2: District Random Variables and Probability Distribution. Prof. Dr. Yunes Mogheir Civil and Environmental Engineering Dept . First Semester/2019.

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Islamic University of Gaza Statistics and Probability for Engineers (ENGC 6310)

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  1. Islamic University of Gaza Statistics and Probability for Engineers (ENGC 6310) Lecture 2: District Random Variables and Probability Distribution Prof. Dr. Yunes Mogheir Civil and Environmental Engineering Dept. First Semester/2019

  2. 3-2 Probability Distributions and Probability Mass Functions Definition

  3. 3-3 Cumulative Distribution Functions Definition

  4. Example 3-8

  5. Example 3-8 Figure 3-4Cumulative distribution function for Example 3-8.

  6. 3-4 Mean and Variance of a Discrete Random Variable Definition

  7. 3-4 Mean and Variance of a Discrete Random Variable Figure 3-5A probability distribution can be viewed as a loading with the mean equal to the balance point. Parts (a) and (b) illustrate equal means, but Part (a) illustrates a larger variance.

  8. 3-4 Mean and Variance of a Discrete Random Variable Figure 3-6The probability distribution illustrated in Parts (a) and (b) differ even though they have equal means and equal variances.

  9. Example 3-11

  10. 3-5 Discrete Uniform Distribution Definition

  11. 3-5 Discrete Uniform Distribution Example 3-13

  12. 3-5 Discrete Uniform Distribution Figure 3-7Probability mass function for a discrete uniform random variable.

  13. 3-5 Discrete Uniform Distribution Mean and Variance

  14. 3-5 Discrete Uniform Distribution

  15. 3-6 Binomial Distribution Random experiments and random variables

  16. 3-6 Binomial Distribution Random experiments and random variables

  17. 3-6 Binomial Distribution Definition

  18. 3-6 Binomial Distribution Figure 3-8Binomial distributions for selected values of n and p.

  19. 3-6 Binomial Distribution Example 3-18

  20. 3-6 Binomial Distribution Example 3-18

  21. 3-6 Binomial Distribution Question

  22. 3-6 Binomial Distribution Mean and Variance

  23. 3-6 Binomial Distribution Example 3-19

  24. 3-7 Geometric Distribution Example 3-20

  25. 3-7 Geometric Distribution Definition

  26. 3-7 Geometric Distribution Figure 3-9. Geometric distributions for selected values of the parameter p.

  27. 3-7 Geometric Distribution 3-7.1 Geometric Distribution Example 3-21

  28. 3-7 Geometric Distribution Definition

  29. 3-7 Geometric Distribution Example 3.22

  30. 3-9 Poisson Distribution Definition

  31. Poisson Distribution • Occurrence of random event in continuous dimension of time and space • Natural disasters • Earthquakes • Request for services (bank, airport, market counters) • Car arrivals at intersection • The probability of x occurrences per unit time • Assumptions • Possible to divide the time interval into very small subintervals so as P( occurrence in each sub-interval is very small ) • P(x) in each sub-interval is constant • P( two or more occurrences in sub-interval ) is ignored • Independent

  32. 3-9 Poisson Distribution Applications: • Intervals: • Length • time, • area, • volume • Counts: • particles of contamination in semiconductor • flaws in rolls of textiles, • calls to a telephone exchange, • power outages, and • atomic particles emitted from a specimen

  33. 3-9 Poisson Distribution Consistent Units

  34. 3-9 Poisson Distribution

  35. 3-9 Poisson Distribution Example 3-33

  36. 3-9 Poisson Distribution Example 3-33

  37. 3-9 Poisson Distribution Mean and Variance

  38. End of lecture 2

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