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Binomial Distribution
Calculate binomial probabilities P(X = k) and cumulative probabilities
P(X = 3)
0.1172
11.72%
With n=10, p=0.5: ~11.7% chance of exactly 3 successes
Mean (μ)
5.00
Variance (σ²)
2.50
Std Dev (σ)
1.58
P(X=k) %
11.72%
Distribution (k vs probability)
About Binomial Distribution
The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. It is one of the most widely used discrete probability distributions in statistics.
P(X = k) = C(n,k) × pk × (1-p)n-k
Where:
• n = number of trials
• k = number of successes
• p = probability of success on each trial
• C(n,k) = binomial coefficient = n! / (k! × (n-k)!)
Key properties:
• Mean (μ) = n × p
• Variance (σ²) = n × p × (1-p)
• Standard Deviation (σ) = √(n × p × (1-p))