%% Excercise 1: % Given the following dataset, which contains the prime numbers less than 100. Dataset2 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]; % 4.1) Compute the sample median. % 4.2) Compute the lower and upper quartiles. %% Excercise 2: % Given the following dataset, which contains Fibonacci numbers less than 100. Dataset3 = [0,1,1,2,3,5,8,13,21,34,55,89]; % 5.1) Compute the standard deviation. % 5.2) Compute the MAD(mean absolute deviation). %% Excercise 3: load poiss.mat. % Let the discrete random variable X be the number of customers visiting % ABC Bank in an hour. We know that X ~ Poiss(lambda). % The poiss.mat stores such information: 1000 records. % 2.1 Estimate lambda; % 2.2 Compute P(X=k), k = minK, minK+1, minK+2, ..., maxK, where minK and maxK % are the minimum and maximum of X, respectively; % 2.3 Estimate P(X=k) by using the frequencies. % 2.4 Plot 2D figure with both results from 1.2 and 1.3: two curves; clear; clc; load poiss.mat; lambda = sum(X)/numel(X); minK = min(X); maxK = max(X); k = minK:1:maxK; p = zeros(1, numel(k)); for i = 1:numel(k) p(i) = lambda^k(i)/factorial(k(i)) * exp(-lambda); end f = zeros(1, numel(k)); [a,b] = histc(X,unique(X)); y = a(b); for i = 1:numel(k) count = 0; for j = 1:numel(X) if k(i) == X(j) count = count + 1; end end f(i) = count/sum(X); end figure plot(p) hold on plot(f) %% Excercise 4: load norm.mat. % Let the continuous random variable X be the price changes of the product XYZ. % Positve values mean its price is increased and negative values mean its % price is decreased. % We know that X ~ N(mu, sigma^2). % The norm.mat stores 1000 records of such information. % Please load the data and % 3.1) Estimate mu and sigma; % 3.2) Compute P(X=a), a belongs to [minX, maxX] where minX and maxX are % the minimum and maximum of X, respectively. % 3.3) Plot a 2D figure. clear; clc; load norm.mat; mu = mean(X); sigma = std(X); minX = min(X); maxX = max(X); p_max = (1/(sigma*sqrt(2*pi)))*exp(-(maxX - mu)^2/2*sigma^2); p_min = (1/(sigma*sqrt(2*pi)))*exp(-(minX - mu)^2/2*sigma^2); norm = normpdf(minX:maxX,mu,sigma^2); figure; plot(minX:maxX,norm) hold on; plot(minX,p_min,'r*'); hold on; plot(maxX,p_max,'r*');