54 lines
1.2 KiB
Mathematica
54 lines
1.2 KiB
Mathematica
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% Joint probability distribution
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P_XY = [0.3, 0.2, 0;
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0.1, 0.15, 0.05;
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0, 0.1, 0.1];
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% Values of X and Y
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X_vals = [0, 1, 2];
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Y_vals = [0, 1, 2];
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% Marginal distributions
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P_X = sum(P_XY, 2);
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P_Y = sum(P_XY, 1);
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% Mean of X and Y
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E_X = sum(X_vals .* P_X');
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E_Y = sum(Y_vals .* P_Y);
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% Variance of X and Y
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Var_X = sum((X_vals - E_X).^2 .* P_X');
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Var_Y = sum((Y_vals - E_Y).^2 .* P_Y);
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% Covariance of X and Y
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E_XY = sum(sum((X_vals' * Y_vals) .* P_XY));
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Cov_XY = E_XY - E_X * E_Y;
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% Correlation coefficient
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rho_XY = Cov_XY / sqrt(Var_X * Var_Y);
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% Display results
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fprintf('Marginal PMF of X: \n');
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disp(P_X');
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fprintf('Marginal PMF of Y: \n');
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disp(P_Y);
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fprintf('Mean of X: %.2f\n', E_X);
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fprintf('Mean of Y: %.2f\n', E_Y);
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fprintf('Variance of X: %.2f\n', Var_X);
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fprintf('Variance of Y: %.2f\n', Var_Y);
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fprintf('Covariance of X and Y: %.2f\n', Cov_XY);
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fprintf('Correlation coefficient between X and Y: %.2f\n', rho_XY);
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% Plot Marginal PMFs
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figure;
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subplot(1,2,1);
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stem(X_vals, P_X, 'filled');
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title('Marginal PMF of X');
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xlabel('X');
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ylabel('P(X)');
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subplot(1,2,2);
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stem(Y_vals, P_Y, 'filled');
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title('Marginal PMF of Y');
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xlabel('Y');
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ylabel('P(Y)');
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