Created by Dr. Pedram Jahangiry | Enhanced with Claude
Interactive Teaching Tool for Understanding Stochastic Processes & Central Limit Theorem
Random Walk Concepts:
• Path Independence: Each walk is unique despite same parameters
• Drift Effect: Positive bias creates upward trend, negative creates downward
• Noise Parameters: Control randomness with mean and variance
Central Limit Theorem Demo:
• Sample Size: Adjust "CLT Sample Size" to see how averaging more walks creates normality
• Step Distribution: Try different distributions - the average still becomes normal!
• Click "Demo CLT": Generates 100 sample means to build the distribution
• Key Insight: Even with non-normal step distributions (exponential, bimodal), the distribution of averages becomes normal!
Mathematical Model:
X(t+1) = X(t) + drift + ε, where ε follows the selected distribution
Sample Mean: X̄ = (X₁ + X₂ + ... + Xₙ)/n → Normal as n increases