Parameters
Adjust the number of trials to see convergence.
10
0.5
Current Gaussian Model
Mean (μ)
--
Std Dev (σ)
--
f(x) =
1
σ√2π
e
-0.5 (
x - μ
σ
)²
Statistics
Mean (μ)
0.00
Std Dev (σ)
0.00
Binomial (Discrete)
Gaussian (Continuous)
k = 15
P(k) = 0.123
nCr = 1540
The Central Limit Theorem
This visualization demonstrates the De Moivre–Laplace theorem, a special case of the Central Limit Theorem. It states that as the number of trials n increases, the probability mass function of the Binomial distribution converges to the probability density function of the Normal (Gaussian) distribution.
Mathematical Relationship
Binomial: P(k) = ⁿCₖ pᵏ(1-p)ⁿ⁻ᵏ
Gaussian: f(x) ≈ e-x²
Notation:
ⁿCᵣ
=
(
n
r
)
Click any bar to see the exact nCr (Combinations) and probability values.