This interactive module demonstrates the convergence of the Binomial distribution to the Poisson distribution when the probability of success p is set as λ / n. As n increases, the Binomial distribution approximates the Poisson distribution more closely.

Objective

• Visualize and quantify how a Binomial distribution with parameters n and p = λ / n converges to a Poisson distribution with mean λ as n increases.

Controls

• Number of trials (n): Adjustable via the slider (between 10 and 1000)
• Poisson mean (λ): Adjustable via the number field (between 0 and 50).
• Note: The value of λ cannot be greater than n.

Visualization

• Binomial PMF — shown in red.
• Poisson PMF — shown in blue.
• Average & Maximum Absolute Error — displayed below the plot.

Interpretation

• As n increases for a fixed λ, the Binomial distribution approaches the Poisson distribution.
• The average and maximum absolute errors quantify the similarity and decrease with larger n.