%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Problem Set 1: Getting started with vectors, functions, and plots in Matlab
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% 1. create vector x, representing the domain of a function
x = -10:0.1:10;

%% 2. write a function 'square' that takes as input a vector x,
%% and oututs a vector y, such that y_i is x_i*x_i.
%% This function should be in an m-file named square.m
%% Use 'help function' to get syntax of matlab functions
%% Use '.*' to do a vector-multiply operation.

y = square(x);

%%3. Plot the results of the above square function using the 'plot' command.
%% Plot the results both as discrete points, and as a continuous line.
%% Use 'help plot' to get the syntax of plot.

%% 4. Adjust the axis of the above plot using the 'axis' command so that x
%% is from -20 to 20, and y is from -200 to 200

%% 5. Create and plot functions for x^2, x^3, x^4, on different axes using the
%% 'subplot' command. Give a title to each of the subplots.

%% 6. Plot functions for x^2, x^3, x^4 on the same axes, in different colors.
%% Use 'hold on' to draw multiple plots.

%%7. Use the 'legend' command to create a legend for the plot in 6.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% uniform pdf
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%8a. Create a function 'uniform(x, a, b)' that takes three inputs:
%% domain vector x, scalar a, scalar b, and returns three outputs:
%% pdf vector u, scalar mean of pdf, scalar variance of pdf
x=[-10:0.1:10];
[u, mu, vu] = uniform(x, -2, 2);

%%8b. Plot the pdf. Adjust axes so that y axis is from 0 to 1.
%% Write the mean and variance on the title bar.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% gaussian pdf
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% 9a. Create a function 'gauss(x, mean, variance)' that takes three inputs:
%% domain vector x, scalar mean, scalar variance, and returns the pdf vector.

g = gauss(x, 0, 1);

%%9b. Plot the pdf with appropriate axes.
%% Write the mean and variance on the title bar.

%%10. Use vectors x and g to compute:
%% a. area under the curve g
%% b. area under the curve g between 0 and 10
%% c. area under the curve g between -2 and 2.
%% Useful commands: 'find(x > -2 & x < -2)'

%%11a. Plot the above uniform and gaussian pdfs on the same plot. Use legend to
%% annotate plot.
%%11b. Create a vector M such that m_i is 0 if u_i > g_i, 1 otherwise.
%% Plot m on the same figure as 11a.