Multinomial Distribution Calculator Online

Probability Sum
0.00 / 1.00
Remaining: 1.00
Successes Sum
0 / 10
Remaining: 10

Results

Descriptive Statistics

Category Mean (μ) Variance (σ²) Std. Deviation (σ)

How to Use

1. Set your Total Trials (n) - the total number of events or samples.

2. Add as many categories as needed. For each, provide the individual Probability (p) and the Successes (x) you wish to calculate for.

3. Ensure the sum of probabilities equals 1.0 and the sum of successes equals your total trials (n).

Theoretical Explanation

The multinomial distribution is used when there are more than two possible outcomes. It calculates the probability of a specific combination of counts for k categories across n independent trials.

\[ P(X_1=x_1, \dots, X_k=x_k) = \frac{n!}{x_1! \dots x_k!} \prod_{i=1}^{k} p_i^{x_i} \]

Mean: Computed as \( n \times p_i \).
Variance: Computed as \( n \times p_i(1 - p_i) \).