73 lines
1.6 KiB
Mathematica
73 lines
1.6 KiB
Mathematica
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%% a)
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% Number of students
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num_students = 120;
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% Mean and variance for N1 and N2
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mu_N1 = 14;
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var_N1 = 3.5;
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mu_N2 = 16.8;
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var_N2 = 4.2;
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% Standard deviations
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sigma_N1 = sqrt(var_N1);
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sigma_N2 = sqrt(var_N2);
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% Generate N1 and N2 from a normal distribution
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N1 = round(normrnd(mu_N1, sigma_N1, [num_students, 1]));
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N2 = round(normrnd(mu_N2, sigma_N2, [num_students, 1]));
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% Ensure values are within a reasonable range (e.g., scores between 0 and 20)
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N1 = max(0, min(20, N1));
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N2 = max(0, min(20, N2));
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%% b)
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% Joint PMF calculation
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joint_counts = zeros(21, 21);
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for i = 1:num_students
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joint_counts(N1(i)+1, N2(i)+1) = joint_counts(N1(i)+1, N2(i)+1) + 1;
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end
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joint_pmf = joint_counts / num_students;
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% Plotting the joint PMF
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[X, Y] = meshgrid(0:20, 0:20);
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figure;
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bar3(joint_pmf);
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xlabel('N_1 scores');
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ylabel('N_2 scores');
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zlabel('Joint Probability');
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title('Joint PMF of N_1 and N_2');
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%% c)
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% Calculate correlation coefficient
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correlation_matrix = corrcoef(N1, N2);
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correlation_coefficient = correlation_matrix(1, 2);
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% Display result
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fprintf('Correlation coefficient between N1 and N2: %.2f\n', correlation_coefficient);
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%% d)
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% Marginal PMFs
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marginal_N1 = sum(joint_pmf, 2);
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marginal_N2 = sum(joint_pmf, 1);
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% Check independence by verifying if joint PMF = product of marginals
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independent = true;
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for i = 1:21
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for j = 1:21
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if abs(joint_pmf(i, j) - (marginal_N1(i) * marginal_N2(j))) > 1e-10
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independent = false;
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break;
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end
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end
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if ~independent
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break;
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end
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end
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% Display independence result
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if independent
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fprintf('N1 and N2 are independent.\n');
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else
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fprintf('N1 and N2 are not independent.\n');
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end
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