43 lines
958 B
Mathematica
43 lines
958 B
Mathematica
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% Joint probability distribution
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P_XY = [1/8, 1/8, 1/24;
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1/8, 1/4, 1/8;
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1/24, 1/8, 1/24];
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% Values of X and Y
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X_vals = [-1, 0, 1];
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Y_vals = [-1, 0, 1];
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% Marginal distributions
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P_X = sum(P_XY, 2); % Sum across rows for X
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P_Y = sum(P_XY, 1); % Sum across columns for Y
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% Checking independence
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independence = true; % Assume independence initially
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for i = 1:length(X_vals)
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for j = 1:length(Y_vals)
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% Calculate product of marginals
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product_marginals = P_X(i) * P_Y(j);
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% Compare with joint probability
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if abs(P_XY(i, j) - product_marginals) > 1e-10
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independence = false;
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break;
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end
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end
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if ~independence
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break;
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end
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end
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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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if independence
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fprintf('X and Y are independent.\n');
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else
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fprintf('X and Y are not independent.\n');
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end
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