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Random Variable

Random Variable. 2013. Random Variable. Two types Discrete Continuous. Random Variable. Probability mass function Discrete P(X = x i ) = p(x i )  p(x i ) = 1. Random Variable. Probability density function Continuous f(x) = e –x x > 0 P(X = a) = 0  -  f(x) dx = 1

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Random Variable

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  1. Random Variable 2013

  2. Random Variable • Two types • Discrete • Continuous

  3. Random Variable • Probability mass function • Discrete • P(X = xi) = p(xi) •  p(xi) = 1

  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

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