CS457 - System Performance Evaluation - Winter 2008

Questions and Comments

  1. Midterm: Q5e
  2. Assignment 3

Lecture 22 - Random Numbers

Text: chapter 12 28 & 29

Random Variables

The mathematical foundation for random number is the random variable, which is a variable that has different values on different occasions.

  1. A probability distribution determines what values a random variable gets, and how often
  2. Discrete versus continuous random variables
  3. We usually assume that the random variables we want are independent and identically distributed (iid or IID).
  4. Most random variables we use have underlying distributions that are non-negative.
  5. Random variables are normally written as capitals.

Random variable concepts

  1. Cumulative distribution function (cdf or CDF):
  2. Probability density function (pdf or PDF):
  3. Probability mass function (pmf or PMF):

In discrete event simulation we model quantities like interarrival time or service time as IID random variables.

As a result we need to generate random variables from random number generators.

Random variables with arbitrary distributions

A random variable is uniquely defined by its CDF, F(x).

Examples of Discrete Distributions

  1. Bernoulli
  2. Discrete uniform
  3. Geometric Discrete
  4. Binomial
  5. Poisson

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