Ohejlma Todennököisyyslaskenta I 2026 kurssia varten: viikko 5 tehtävä 5.

Fraction.java

package viikko5;

import java.util.Objects;

public final class Fraction implements Comparable<Fraction> {

    public static final Fraction ZERO = new Fraction(0);
    
    private final long numerator;
    private final long denominator;

    public Fraction(long numerator, long denominator) {
        if (denominator == 0) {
            throw new ArithmeticException("Denominator cannot be zero.");
        }

        // Normalize sign (denominator always positive)
        if (denominator < 0) {
            numerator = -numerator;
            denominator = -denominator;
        }

        long gcd = gcd(Math.abs(numerator), denominator);
        this.numerator = numerator / gcd;
        this.denominator = denominator / gcd;
    }
    
    public Fraction(long number) {
        this(number, 1L);
    }

    public static Fraction of(long numerator, long denominator) {
        return new Fraction(numerator, denominator);
    }
    
    public static Fraction of(long number) {
        return of(number, 1L);
    }

    public long getNumerator() {
        return numerator;
    }

    public long getDenominator() {
        return denominator;
    }

    /* ================= Arithmetic ================= */

    public Fraction add(Fraction other) {
        long num = this.numerator * other.denominator
                 + other.numerator * this.denominator;
        long den = this.denominator * other.denominator;
        return new Fraction(num, den);
    }

    public Fraction subtract(Fraction other) {
        long num = this.numerator * other.denominator
                 - other.numerator * this.denominator;
        long den = this.denominator * other.denominator;
        return new Fraction(num, den);
    }

    public Fraction multiply(Fraction other) {
        return new Fraction(
                this.numerator * other.numerator,
                this.denominator * other.denominator
        );
    }

    public Fraction divide(Fraction other) {
        if (other.numerator == 0) {
            throw new ArithmeticException("Division by zero fraction.");
        }

        return new Fraction(
                this.numerator * other.denominator,
                this.denominator * other.numerator
        );
    }

    public Fraction negate() {
        return new Fraction(-numerator, denominator);
    }

    public Fraction reciprocal() {
        if (numerator == 0) {
            throw new ArithmeticException("Zero has no reciprocal.");
        }
        return new Fraction(denominator, numerator);
    }
    
    public double asDouble() {
        return (double) numerator / (double) denominator;
    }

    /* ================= Comparison ================= */

    @Override
    public int compareTo(Fraction other) {
        // Avoid floating-point comparison
        return Long.compare(
                this.numerator * other.denominator,
                other.numerator * this.denominator
        );
    }

    @Override
    public boolean equals(Object obj) {
        if (this == obj) return true;
        if (!(obj instanceof Fraction)) return false;
        Fraction other = (Fraction) obj;
        return numerator == other.numerator &&
               denominator == other.denominator;
    }

    @Override
    public int hashCode() {
        return Objects.hash(numerator, denominator);
    }

    @Override
    public String toString() {
        if (denominator == 1) {
            return Long.toString(numerator);
        }
        return numerator + "/" + denominator;
    }
    
    public String toTexDollar() {
        return "$\\frac{" + numerator + "}{" + denominator + "}$";
    }
    
    public String toTex() {
        return "\\frac{" + numerator + "}{" + denominator + "}";
    }

    /* ================= Utilities ================= */

    private static long gcd(long a, long b) {
        while (b != 0) {
            long tmp = b;
            b = a % b;
            a = tmp;
        }
        return a;
    }
}

Tehtavat5.java

package viikko5;

import java.util.HashMap;
import java.util.Map;

public class Tehtavat5 {
    
    public static void tehtava5() {
        Map<Integer, Map<Integer, Fraction>> m = new HashMap<>();
        
        for (int s = 2; s <= 12; ++s) {
            m.put(s, new HashMap<>());
            
            for (int x = 1; x <= 6; ++x) {
                m.get(s).put(x, Fraction.ZERO);
            }
        }
        
        // Table initialized!
        
        for (int s = 2; s <= 12; ++s) {
            for (int b = 1; b <= 6; ++b) {
                int a = s - b;
                Fraction p = 
                        (1 <= a && a <= 6
                        ? Fraction.of(1, 36) 
                        : Fraction.ZERO);
                
                m.get(s).put(b, p);
            }
        }
        
        for (int j = 2; j <= 12; ++j) {
            System.out.printf("%2d & ", j);
            
            for (int i = 1; i <= 6; ++i) {
                
                if (i > 1) {
                    System.out.print("& ");
                }
                
                Fraction p = m.get(j).get(i);
                System.out.print(p);
            }
            
            Fraction rs = rowSum(m, j);
            System.out.printf(" & %s \\\\%n", rs);
        }
        
        printColumnSums(m);
        printRowWiseTotal(m);
        System.out.println("Poikkeavat todennäköisyydet:");
        printDifferentEtnries(m);
        printSubtaskCProbability(m);
    }
    
    private static void printRowWiseTotal(
            Map<Integer, Map<Integer, Fraction>> m) {
        
        System.out.println();
        Fraction total = Fraction.ZERO;
        
        for (int s = 2; s <= 12; ++s) {
            total = total.add(rowSum(m, s));
        }
        
        System.out.println(total);
    }
    
    private static void printColumnSums(
            Map<Integer, Map<Integer, Fraction>> m) {
        
        System.out.print("  ");
        Fraction total = Fraction.ZERO;
        
        for (int b = 1; b <= 6; ++b) {
            Fraction s = columnSum(m, b);
            total = total.add(s);
            System.out.printf(" & %s", s);
        }
        
        System.out.printf(" & %s \\\\", total);
    }
    
    private static Fraction columnSum(Map<Integer, Map<Integer, Fraction>> m, 
                                      int b) {
        Fraction sum = Fraction.ZERO;
        
        for (int y = 2; y <= 12; ++y) {
            Map<Integer, Fraction> mm = m.get(y);
            sum = sum.add(mm.get(b));
        }
        
        return sum;
    }
    
    private static Fraction rowSum(Map<Integer, Map<Integer, Fraction>> m, 
                                   int row) {
        Fraction sum = Fraction.ZERO;
        
        for (Fraction f : m.get(row).values()) {
            sum = sum.add(f);
        }
        
        return sum;
    }
    
    private static Fraction fx(int x, Map<Integer, Map<Integer, Fraction>> m) {
        Fraction s = Fraction.ZERO;
        
        for (Map<Integer, Fraction> row : m.values()) {
            s = s.add(row.get(x));
        }
        
        return s;
    }
    
    private static Fraction fy(int y, Map<Integer, Map<Integer, Fraction>> m) {
        Fraction s = Fraction.ZERO;
        
        Map<Integer, Fraction> mm = m.get(y);
        
        for (Fraction d : mm.values()) {
            s = s.add(d);
        }
        
        return s;
    }
    
    private static void printDifferentEtnries(
            Map<Integer, Map<Integer, Fraction>> m) {
        int rowNumber = 1;
        
        for (int y = 2; y <= 12; ++y) {
            for (int x = 1; x <= 6; ++x) {
                Fraction fxy = m.get(y).get(x);
                Fraction fx  = fx(x, m);
                Fraction fy  = fy(y, m);
                Fraction fxfy = fx.multiply(fy);
                
                if (!fxfy.equals(fxy)) {
                    System.out.printf(
                            "Rivi %2d: x = %d, y = %d: %s vs %s\n",
                            rowNumber++,
                            x,
                            y,
                            fxfy,
                            fxy);
                }
            }
        }
    }
    
    private static void 
        printSubtaskCProbability(Map<Integer, Map<Integer, Fraction>> m) {
        Fraction ex = ex(m);
        Fraction ey = ey(m);
        Fraction varx = varx(m, ex);
        Fraction vary = vary(m, ey);
        Fraction cov  = cov(m, ex, ey);
        double corr = cov.asDouble() / 
                (Math.sqrt(varx.asDouble() * vary.asDouble()));
        
        System.out.println("Corr(X, Y) = " + corr);
    }
    
    private static Fraction ex(Map<Integer, Map<Integer, Fraction>> m) {
        Fraction fp = Fraction.ZERO;
        
        for (int x = 1; x <= 6; ++x) {
            fp = fp.add(Fraction.of(x).multiply(fx(x, m)));
        }
        
        System.out.println();
        return fp;
    }
    
    private static Fraction ey(Map<Integer, Map<Integer, Fraction>> m) {
        Fraction fp = Fraction.ZERO;
        
        for (int y = 2; y <= 12; ++y) {
            fp = fp.add(Fraction.of(y).multiply(fy(y, m)));
        }
        
        System.out.println();
        return fp;
    }
    
    private static Fraction varx(Map<Integer, Map<Integer, Fraction>> m,
                                 Fraction ex) {
        Fraction fp = Fraction.ZERO;
        
        for (int x = 1; x <= 6; ++x) {
            Fraction t = Fraction.of(x).subtract(ex);
            Fraction pow = t.multiply(t);
            fp = fp.add(pow.multiply(fx(x, m)));
        }
        
        return fp;
    }
    
    private static Fraction vary(Map<Integer, Map<Integer, Fraction>> m,
                                 Fraction ey) {
        Fraction fp = Fraction.ZERO;
        
        for (int y = 2; y <= 12; ++y) {
            Fraction t = Fraction.of(y).subtract(ey);
            Fraction pow = t.multiply(t);
            fp = fp.add(pow.multiply(fy(y, m)));
        }
        
        return fp;
    }
    
    private static Fraction cov(Map<Integer, Map<Integer, Fraction>> m,
                                Fraction ex,
                                Fraction ey) {
        Fraction fp = Fraction.ZERO;
        
        for (int x = 1; x <= 6; ++x) {
            for (int y = 2; y <= 12; ++y) {
                Fraction term1 = Fraction.of(x).subtract(ex);
                Fraction term2 = Fraction.of(y).subtract(ey);
                fp = fp.add(term1.multiply(term2).multiply(m.get(y).get(x)));
            }
        }
        
        return fp;
    }
        
    public static void main(String[] args) {
        tehtava5();
    }
}