[ADD] : maths joint probabilty distribution (#10508)

* Create joint_probability_distribution.py

* Update joint_probability_distribution.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update joint_probability_distribution.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update joint_probability_distribution.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update joint_probability_distribution.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update joint_probability_distribution.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update joint_probability_distribution.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update joint_probability_distribution.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update joint_probability_distribution.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update joint_probability_distribution.py

* Update joint_probability_distribution.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update joint_probability_distribution.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update joint_probability_distribution.py

* Update joint_probability_distribution.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update maclaurin_series.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Revert changes to maclaurin_series.py

* Revert changes to maclaurin_series.py

* Update joint_probability_distribution.py

* Update joint_probability_distribution.py

* Update joint_probability_distribution.py

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

maths/joint_probability_distribution.py

@@ -0,0 +1,124 @@
+"""
+Calculate joint probability distribution
+https://en.wikipedia.org/wiki/Joint_probability_distribution
+"""
+
+
+def joint_probability_distribution(
+    x_values: list[int],
+    y_values: list[int],
+    x_probabilities: list[float],
+    y_probabilities: list[float],
+) -> dict:
+    """
+    >>> joint_distribution =  joint_probability_distribution(
+    ...     [1, 2], [-2, 5, 8], [0.7, 0.3], [0.3, 0.5, 0.2]
+    ... )
+    >>> from math import isclose
+    >>> isclose(joint_distribution.pop((1, 8)), 0.14)
+    True
+    >>> joint_distribution
+    {(1, -2): 0.21, (1, 5): 0.35, (2, -2): 0.09, (2, 5): 0.15, (2, 8): 0.06}
+    """
+    return {
+        (x, y): x_prob * y_prob
+        for x, x_prob in zip(x_values, x_probabilities)
+        for y, y_prob in zip(y_values, y_probabilities)
+    }
+
+
+# Function to calculate the expectation (mean)
+def expectation(values: list, probabilities: list) -> float:
+    """
+    >>> from math import isclose
+    >>> isclose(expectation([1, 2], [0.7, 0.3]), 1.3)
+    True
+    """
+    return sum(x * p for x, p in zip(values, probabilities))
+
+
+# Function to calculate the variance
+def variance(values: list[int], probabilities: list[float]) -> float:
+    """
+    >>> from math import isclose
+    >>> isclose(variance([1,2],[0.7,0.3]), 0.21)
+    True
+    """
+    mean = expectation(values, probabilities)
+    return sum((x - mean) ** 2 * p for x, p in zip(values, probabilities))
+
+
+# Function to calculate the covariance
+def covariance(
+    x_values: list[int],
+    y_values: list[int],
+    x_probabilities: list[float],
+    y_probabilities: list[float],
+) -> float:
+    """
+    >>> covariance([1, 2], [-2, 5, 8], [0.7, 0.3], [0.3, 0.5, 0.2])
+    -2.7755575615628914e-17
+    """
+    mean_x = expectation(x_values, x_probabilities)
+    mean_y = expectation(y_values, y_probabilities)
+    return sum(
+        (x - mean_x) * (y - mean_y) * px * py
+        for x, px in zip(x_values, x_probabilities)
+        for y, py in zip(y_values, y_probabilities)
+    )
+
+
+# Function to calculate the standard deviation
+def standard_deviation(variance: float) -> float:
+    """
+    >>> standard_deviation(0.21)
+    0.458257569495584
+    """
+    return variance**0.5
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
+    # Input values for X and Y
+    x_vals = input("Enter values of X separated by spaces: ").split()
+    y_vals = input("Enter values of Y separated by spaces: ").split()
+
+    # Convert input values to integers
+    x_values = [int(x) for x in x_vals]
+    y_values = [int(y) for y in y_vals]
+
+    # Input probabilities for X and Y
+    x_probs = input("Enter probabilities for X separated by spaces: ").split()
+    y_probs = input("Enter probabilities for Y separated by spaces: ").split()
+    assert len(x_values) == len(x_probs)
+    assert len(y_values) == len(y_probs)
+
+    # Convert input probabilities to floats
+    x_probabilities = [float(p) for p in x_probs]
+    y_probabilities = [float(p) for p in y_probs]
+
+    # Calculate the joint probability distribution
+    jpd = joint_probability_distribution(
+        x_values, y_values, x_probabilities, y_probabilities
+    )
+
+    # Print the joint probability distribution
+    print(
+        "\n".join(
+            f"P(X={x}, Y={y}) = {probability}" for (x, y), probability in jpd.items()
+        )
+    )
+    mean_xy = expectation(
+        [x * y for x in x_values for y in y_values],
+        [px * py for px in x_probabilities for py in y_probabilities],
+    )
+    print(f"x mean: {expectation(x_values, x_probabilities) = }")
+    print(f"y mean: {expectation(y_values, y_probabilities) = }")
+    print(f"xy mean: {mean_xy}")
+    print(f"x: {variance(x_values, x_probabilities) = }")
+    print(f"y: {variance(y_values, y_probabilities) = }")
+    print(f"{covariance(x_values, y_values, x_probabilities, y_probabilities) = }")
+    print(f"x: {standard_deviation(variance(x_values, x_probabilities)) = }")
+    print(f"y: {standard_deviation(variance(y_values, y_probabilities)) = }")