STAT417 Project 3

Description

A computer system is shared by 2 users who work independently. At any given moment, either user can:

• disconnect from the system, with probability = 0.5
• connect wto the system, with probability = 0.2

The number of users can be 0, 1, or 2, forming a Markov chain with 3 states. The task is to simulate 10,000 transitions of this Markov chain and determine what percentage of the time the system is in each of the 3 states.

Simulated Data

##  [1] 0 0 1 0 0 0 0 1 0 2 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0
## [39] 0 2 1 1 0 1 1 1 0 0 1 0

Frequency Table

##   State Frequency
## 1     0      5071
## 2     1      4112
## 3     2       817

##   State Percentage
## 1     0      50.71
## 2     1      41.12
## 3     2       8.17

Bar Graph of Simulated Data

Findings

Based on the frequency table and bar graph of the simulated data, it appears that from the 10,000 generated transitions:

• State 0 (0 users connected) had the highest frequency of 5,185, or 51.85%.
• State 1 (1 user connected) had a frequency of 4,027, or 40.27%.
• State 2 (2 users connected) had the lowest frequency of 788, or 7.88%.

From this data, we can conclude that at any given time, the probability of having 0 users connected (state 0) is the highest at 51.85%, and the probability of having 2 users connected (state 2) is the lowest at 7.88%.