1. 540201 Statistics for Engineer Week II and Week III: Random Variables and Probability Distribution

2. Random Variables 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. Continuous Uniform Distribution

13. 3-5.1 Normal Distribution (Gaussian)

14. Normal Distribution

17. Ex 3-11 Ex 3-12

18. Normal Distribution

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

21. t-Distribution

22. Exponential Distribution

24. 3-7 Discrete Random Variables Probability Mass Function (pmf)

25. Discrete Random Variables Cumulative Distribution Function (cdf)

26. Discrete Random Variables Mean and Variance

27. 3-8 Binomial Distribution A Bernoulli Trial

28. Binomial Distribution

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

30. 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

31. 3-9 Poison Distribution

34. 3-10 Normal Approximation to the Binomial and Poisson Distributions Normal Approximation to the Binomial

35. 3-10 Normal Approximation to the Binomial and Poisson Distributions

37. Normal Approximation to the Poisson

38. 3-10 Normal Approximation to the Binomial and Poisson Distributions

40. Q &A