Gezamenlijke, Marginale en Conditionele Kansen

import numpy as np
import pandas as pd
import plotly.express as px
import plotly.graph_objects as go
from plotly.subplots import make_subplots
from scipy import stats

# Set random seed
rng = np.random.default_rng(42)

# Create joint probability table for weather and transportation mode
# X: Weather (1=Sunny, 2=Cloudy, 3=Rainy)
# Y: Transportation (1=Walking, 2=Car, 3=Tram/Bus, 4=Train)

# Define the joint probability matrix
# People walk more when sunny, use car/bus more when rainy
joint_prob = np.array(
    [
        [0.20, 0.10, 0.12, 0.08],  # Sunny (P(x=1) = 0.50)
        [0.10, 0.08, 0.08, 0.04],  # Cloudy (P(x=2) = 0.30)
        [0.03, 0.07, 0.07, 0.03],  # Rainy (P(x=3) = 0.20)
    ]
)

weather_labels = ["Zonnig", "Bewolkt", "Regenachtig"]
transport_labels = ["Te voet", "Auto", "Tram/Bus", "Trein"]

# Create DataFrame for better visualization
joint_df = pd.DataFrame(
    joint_prob,
    index=[f"{w} (x={i + 1})" for i, w in enumerate(weather_labels)],
    columns=[f"{t} (y={j + 1})" for j, t in enumerate(transport_labels)],
)

print("Joint Probability Distribution P(x, y):")
print(joint_df)
print(f"\nTotal probability: {joint_prob.sum():.1f}")

# 1. P(x=1, y=1) - Sunny and Walking
p_sunny_walking = joint_prob[0, 0]
print(f"1. P(x=1, y=1) = P(Zonnig, Te voet) = {p_sunny_walking:.3f}")

# 2. P(x=3, y∈{2,3}) - Rainy and (Car OR Tram/Bus)
p_rainy_car_or_bus = joint_prob[2, 1] + joint_prob[2, 2]
print(f"2. P(x=3, y∈{{2,3}}) = P(Regenachtig, Auto of Tram/Bus) = {p_rainy_car_or_bus:.3f}")

# 3. P(y=4) - Train (regardless of weather) - this is marginal probability
p_train = joint_prob[:, 3].sum()
print(f"3. P(y=4) = P(Trein) = {p_train:.3f}")

# Calculate marginal distributions
marginal_x = joint_prob.sum(axis=1)  # sum over y (columns) - weather distribution
marginal_y = joint_prob.sum(axis=0)  # sum over x (rows) - transport distribution

print("Marginal distribution P(x) - Weertype:")
for i, (weather, prob) in enumerate(zip(weather_labels, marginal_x, strict=False), start=1):
    print(f"  P(x={i}) = P({weather}) = {prob:.3f}")

print("\nMarginal distribution P(y) - Verplaatsingsmodus:")
for j, (transport, prob) in enumerate(zip(transport_labels, marginal_y, strict=False), start=1):
    print(f"  P(y={j}) = P({transport}) = {prob:.3f}")

print(f"\nVerification:")
print(f"  Sum of P(x): {marginal_x.sum():.1f}")
print(f"  Sum of P(y): {marginal_y.sum():.1f}")

# Conditional distribution P(y | x in {2, 3}) - Transport mode given Cloudy or Rainy weather
x_values = [2, 3]  # Cloudy or Rainy
x_indices = [x - 1 for x in x_values]

# P(y | x in {2, 3}) = P(x in {2, 3}, y) / P(x in {2, 3})
conditional_y_given_cloudy_or_rainy = (
    joint_prob[x_indices, :].sum(axis=0) / marginal_x[x_indices].sum()
)

print(
    f"Conditional distribution P(y | x={x_values}) - Verplaatsingsmodus gegeven Bewolkt of Regenachtig weer:"
)
for j, (transport, prob) in enumerate(
    zip(transport_labels, conditional_y_given_cloudy_or_rainy, strict=False), start=1
):
    print(f"  P(y={j} | x={x_values}) = P({transport} | Bewolkt of Regen) = {prob:.4f}")

print(f"\nVerification: sum = {conditional_y_given_cloudy_or_rainy.sum():.1f}")

# Compare with marginal - they should be different (variables are dependent)
print("\nComparison with marginal P(y):")
print(f"  P(y|x={x_values}) ≈ P(y)? {np.allclose(conditional_y_given_cloudy_or_rainy, marginal_y)}")
print(
    f"  → Variables are {'independent' if np.allclose(conditional_y_given_cloudy_or_rainy, marginal_y) else 'dependent'}!"
)