1. Random Variable
2013

2. Random Variable
Two types
Discrete
Continuous

3. Random Variable Probability mass function Discrete P(X = xi) = p(xi)

4. Random Variable Probability density function Continuous
f(x) = e –x x > 0
P(X = a) = 0
-  f(x) dx = 1
P(a < x < b) = ab f(x) dx

5. Random Variable Expected value  = E(x)  =  xi p (xi)
 =  x f(x) dx

6. Random Variable
Variance

7. Random Variable
Standard deviation
Sums of R.V.

8. Random Variable

9. Poisson Probability Distribution

10. Poisson Probability Distribution

11. Exponential Distribution

12. Exponential Distribution

13. The Uniform Distribution

14. The Uniform Distribution

15. The Uniform Distribution

16. The Triangular Distribution
Continuous Distribution

17. The Triangular Distribution

18. The Triangular Distribution

19. Normal Distribution

20. Normal Distribution

21. Normal Distribution

22. Normal Distribution

23. Selecting a Distribution
Theoretical prior knowledge
Random arrival => exponential IAT
Sum of large manufactures => Normal CLT
Compare histogram with probability mass or probability density