MATLAB A# 1

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Programming Assignment: Probability

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Instructions

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% This file contains code that helps you get started on the

% probability assignment.

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% For this part of the exercise, you will need to change some

% parts of the code below for various experiments.

%

% Initialization

rng(“default”);

%% ================ Part 1: Toss a coin ===================

% Instructions: Define a random variable called “coin” that represents the coin,

% i.e., it can take two possible values, 0 (tail)

% and 1 (head), with the probability of taking each

% value being 0.5.

% Then, complete the following steps.

% Step 1: toss a coin once, and show the value of the

% coin

% Step 2: toss a coin for 10 times, count the

% number of heads. Store the number of

% heads in variable “c” and print its value

% ============================================================

fprintf(‘===== Part 1: Toss a coin ===== \n’);

% ====================== YOUR CODE HERE ======================

% Step 1: toss a coin, and show the value of the coin

fprintf(‘Toss a coin …\n’);

fprintf(‘The value of the coin: \n %s\n’, coin);

% Step 2: toss a coin for 10 times and count the number of heads

% Store the number of heads in variable “c” and print its value

fprintf(‘Toss a coin for 10 times …\n’);

fprintf(‘The number of heads: \n %d\n’, c);

% ============================================================

fprintf(‘Program paused. Press enter to continue.\n’);

pause;

%% ================ Part 2: Roll a die ================

% Instructions: Define a random variable “die” that represents the die,

% i.e., it can take six possible values, 0 – 6, with

% the probability of taking each value being 1/6.

% Then, complete the following steps.

% Step 1: roll a die once

, and show its value

% Step 2: roll a die for 10 times and make a histogram

% showing the distribution (Hint: can use

% function “hist()” to plot the histogram)

% Step 3: roll a die for 10000 times, make a histogram,

% and then plot an empirical cdf (Hint: can use

% function “stairs()” to plot the cdf)

% ============================================================

fprintf(‘===== Part 2: Roll a die ===== \n’);
% ====================== YOUR CODE HERE ======================

% Step 1: roll a die once

fprintf(‘Roll a die …\n’);

fprintf(‘The value of the die: \n %s\n’, die);

% Step 2: roll a die 10 times and make a histogram

fprintf(‘Roll a die 10 times …\n’);

fprintf(‘Showing the histogram of the die…\n’);

% Step 3: roll a die 10000 times, make a histogram, and plot the cdf

fprintf(‘Roll a die 10000 times …\n’);

fprintf(‘Showing the empiral cdf of the die…\n’);

% ============================================================fprintf(‘Program paused. Press enter to continue.\n’);pause;

%% ================ Part 3: Plot a normal distribution ================

% Instructions: Generate 10000 random samples from the normal distribution

% with mean = 1 and variance = 4 (Hint: use function “rand()”).

% Define the variable name as “ND”, e.g.: ND = ….

% Then complete the following:

% Step 1: Make a histogram to show the distribution.

% Step 2: Fit a probability density function (normal distribution)

% to the data and plot the pdf superimposed over a histogram

% of the data (Hint: use function “fitdist()”)

% ============================================================

fprintf(‘===== Part 3: Plot a normal distribution ===== \n’);

% ====================== YOUR CODE HERE ======================% Step 1: Make a histogram to show the distribution.

fprintf(‘Showing the histogram of the data …\n’);

% Step 2: Fit a probability density function to the data and plot the pdf

% superimposed over a histogram of the data (Hint: use function “fitdist()”)

fprintf(‘Showing the pdf created by fitting a normal distribution to the data …\n’);

% ============================================================