20-12-2012, 03:21 PM
Theory and Problems of Probability, Random Variables, and Random
1Theory and Problems.pdf (Size: 4.5 MB / Downloads: 89)
INTRODUCTION
The study of probability stems from the analysis of certain games of chance, and it has found
applications in most branches of science and engineering. In this chapter the basic concepts of probability
theory are presented.
SAMPLE SPACE AND EVENTS
A. Random Experiments:
In the study of probability, any process of observation is referred to as an experiment. The results
of an observation are called the outcomes of the experiment. An experiment is called a random experiment
if its outcome cannot be predicted. Typical examples of a random experiment are the roll of a
die, the toss of a coin, drawing a card from a deck, or selecting a message signal for transmission from
several messages.
THE M/M/1 QUEUEING SYSTEM
In the M/M/1 queueing system, the arrival process is the Poisson process with rate A (the mean
arrival rate) and the service time is exponentially distributed with parameter p (the mean service rate).
Then the process N(t) describing the state of the M/M/1 queueing system at time t is a birth-death
process with the Following state independent parameters.