Intro to Python & Random Number Generation

2. Context
Both wired and wireless data networks have some degree of randomness that affect their operation.
Examples of such randomness are the packet loss probability during transmission, random back-off
times before transmission/re-transmission on a shared medium, buffer overflow errors due to
congestion, etc. Such random parameters are usually modeled in simulation using randomly generated
numbers from probability distributions that match the observed behavior in real life.
3. Objectives
The objective of this first lab is to set-up and familiarize yourself with the Python programming
environment. More precisely, the main task in this first lab is to generate random numbers from
different probability distributions using existing libraries and calculate various statistics.

4. Manipulations/Questions
4.1) List a few processes related to computer networks that involve randomness.
4.2) Using the built-in functions from Python, generate random numbers from the standard Uniform
distribution
. Generate 10, 100, 1000, 10000 and 100000 random numbers using a seed of 5. For each
set of generated random numbers:
Plot a histogram with 30 bins. Your histogram should show the number of occurrences
in each bin.
Calculate the mean
Calculate the variance
Calculate the standard deviation
4.3) Using the random.exponential function, repeat Step 4.2 for the Exponential distribution with a
rate (
𝜆) of 1/5.
Note: Different function implementations exist in Python for generating the Exponential
distribution. Some use the “rate” parameter, which is the average number of arrivals during a
certain time interval, while others use the “scale” parameter, which is 1/rate. Make sure you
use the correct parameter in your function.
4.4) Repeat Step 4.2 for the Poisson distribution with a mean of 5.
FYI: The Exponential distribution is a continuous distribution that is often used to model the
interarrival times between randomly occurring events (like the interarrival times between
customers walking into a store), while the Poisson distribution is a discrete distribution that is
often used to model the number of random events during a fixed time interval (like the number
of customers in an hour).
4.5) What is the goal of plotting histograms?
4.6) Based on the Uniform and Exponential distributions that you used previously, what should be the
theoretical mean?
4.7) What is the effect on the accuracy of the results as we generate more numbers? Justify your
answer with the results from the previous questions.
5. Lab report
Your lab report (one report per team) should contain the following:
A cover page with your names, student IDs, and lab number.
Answers to all questions/manipulations from Section 4.
Your source files (code) used to complete this lab.

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