Probability Distributions
Interactive exploration of binomial and normal distributions
Explore probability distributions by adjusting parameters and running simulations. Compare theoretical distributions with experimental results from virtual dice rolls!
Binomial Distribution
Normal Distribution
Distribution Statistics:
Theoretical Mean: 5.0
Theoretical Standard Deviation: 1.581
Simulation Mean: -
Simulation Standard Deviation: -
Current Distribution:
The binomial distribution describes the number of successes in a fixed number of independent trials, each with the same probability of success.
PMF: P(X=k) = C(n,k) × pᵏ × (1-p)ⁿ⁻ᵏ
Understanding Probability Distributions
Key Concepts:
Probability distributions describe how probabilities are distributed over the values of a random variable:
- Binomial Distribution: Models counts of binary outcomes (success/failure) in fixed trials
- Normal Distribution: Models continuous data that clusters around a mean
- Mean: The average or expected value of the distribution
- Standard Deviation: Measures how spread out the values are
Real-world Applications:
- Binomial: Quality control (defective items), coin flips, survey responses
- Normal: Heights of people, test scores, measurement errors
