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CSE 3504: Probabilistic Analysis of Computer Systems

CSE 3504: Probabilistic Analysis of Computer Systems. Topics covered: Multiple random variables Transform methods (Sec. 4.1-4.2, 4.5.7). Sum of random variables: Expectation. Expectation of a sum of two random variables: Expectation of a sum of n random variables:

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CSE 3504: Probabilistic Analysis of Computer Systems

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  1. CSE 3504: Probabilistic Analysis of Computer Systems Topics covered: Multiple random variables Transform methods (Sec. 4.1-4.2, 4.5.7)

  2. Sum of random variables: Expectation • Expectation of a sum of two random variables: • Expectation of a sum of n random variables: • Special case: All the random variables have the same mean

  3. Sum of random variables: Expectation • Alternate expression for variance:

  4. Sum of random variables: Expectation • Example: Variance of the number of heads in a sequence of three coin tosses

  5. Sum of random variables: Variance • Exponential random variable:

  6. Sum of random variables: Variance

  7. Moment generating function • Definition:

  8. Moment generating function (contd..) • Laplace-Stilje’s transform:

  9. Moment generating function (contd..) • Probability Generating Function:

  10. Moment generating function (contd..) • How to use these functions:

  11. Moment generating function (contd..) • Laplace-Stilje’s transform of the exponential distribution:

  12. Moment generating function (contd..) • Convolution theorem:

  13. Moment generating function (contd..) • Sum of exponential random variables (Erlang distribution):

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