1. 1/2555 สมศักดิ์ ศิวดำรงพงศ์ somsaksi@sut.ac.th
Statistics and Numerical Method Part I: Statistics Week III: Random Variables and Probability Distribution
1/2555
สมศักดิ์ ศิวดำรงพงศ์

2. Random Variables Controllable Variables Output Input
Uncontrollable Variables
Controllable Variables
Output
Random Variable : A Numerical variable whose measured value can change from one replicate of the experiment to another

3. 3-2 Random Variables Discrete random variables
Continuous random variables

4. 3-3 Probability The chance of “x” A degree of belief
A relative frequency between “event frequency” to the “outcome frequency”

5. 3-4 Continuous Random Variables
Cumulative Distribution Function (cdf)

6. Continuous Random Variables
Probability Density Function (pdf)

7. Continuous Random Variables
Mean and Variance

8. Example 3.5

9. 3-5.1 Normal Distribution (Gaussian)

10. Normal Distribution

11. Normal Distribution

12. Normal Distribution

13. Normal Distribution

14. Normal Distribution

15. t-Distribution When  is unknown Small sample size
Degree of freedom (k) = n-1
Significant level = 
t, k

16. t-Distribution

17. 3-7 Discrete Random Variables
Probability Mass Function (pmf)

18. Discrete Random Variables
Cumulative Distribution Function (cdf)

19. Discrete Random Variables
Mean and Variance

20. 3-8 Binomial Distribution
A Bernoulli Trial

21. Binomial Distribution

22. Binomial Distribution
Example 3-28 Bit transmission errors: Binomial Mean and Variance

23. 3-9 Poison Distribution
The random variable X that equals the number of events in a Poison process is a Poison random variable with parameter >0, and the probability mass function of X is
The mean and variance of X are

24. 3-9 Poison Distribution

25. 3-9 Poison Distribution

26. 3-9 Poison Distribution

27. 3-10 Normal Approximation to the Binomial and Poisson Distributions

28. 3-10 Normal Approximation to the Binomial and Poisson Distributions

29. 3-10 Normal Approximation to the Binomial and Poisson Distributions
Normal Approximation to the Poisson

30. 3-13 Random Samples, Statistics and the Central Limit Theorem

31. 3-13 Random Samples, Statistics and the Central Limit Theorem

32. 3-13 Random Samples, Statistics and the Central Limit Theorem

33. 3-13 Random Samples, Statistics and the Central Limit Theorem

34. Q &A