Computer Lab Four Probability #1

In this computer lab we are going to investigate the how we can work with random variables and probability distributions using MATLAB.

We will be using a number of inbuilt MATLAB functions to perform this analysis and will be using the function histogram to analyse the results we obtain. It is possible to normalise the output of the histogram function into a probability distribution function (PDF) using the function parameters histogram(_,'Normalization','pdf').

Question 1

Use the rand function to simulate a coin toss 50 times. Use the histogram function and an appropriate normalisation technique to find out the probability of the result being heads. What happens to the probability as the number of tries increases? What function might you use to ensure repeatability of your code?

Question 2

Use the randi function to simulate the roll of a fair dice 100 times. Use the histogram function and an appropriate normalisation technique to find out the probability of the result being 3. What happens to the probability as the number of dice rolls increases?

Question 3

Use the randn function to generate vectors of normalised Gaussian noise (mean 0, variance 1) for 10, 100, 1000, and 10000 points. Use the histogram function to inspect the histogram of each vector. What happens as the number of points in the noisy data increases? Model the equation of a Gaussian function and plot it over the histogram. What can you conclude?

Question 4

Assume that on average 5 communications packets arrive at a computer every second. Using the poisspdf function determine the probability that 0 to 10 packets will arrive in any given one second interval. Plot these probabilities on an appropriately labelled graph. Is it possible to model fractional packet arrival using this methodology? Why or why not?