1. What Is Binomial Distribution Variance?

The variance of a binomial distribution measures how spread out the distribution is. It quantifies the variability of outcomes in repeated Bernoulli trials.

2. How The Calculator Works

The calculator uses the binomial variance formula:

Where:

• \( n \) — Number of trials
• \( p \) — Probability of success on each trial

Explanation: The variance increases with more trials (n) and is maximized when p = 0.5. It decreases as p approaches 0 or 1.

3. Importance of Variance Calculation

Details: Understanding variance helps assess the reliability of expected outcomes and is crucial for statistical inference, quality control, and risk assessment.

4. Using The Calculator

Tips: Enter number of trials (positive integer) and probability (between 0 and 1). The calculator will compute the variance of the binomial distribution.

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between variance and standard deviation?
A: Standard deviation is the square root of variance. Both measure spread but in different units.

Q2: When is variance maximized in binomial distribution?
A: Variance is maximized when p = 0.5, for any given n.

Q3: What does zero variance mean?
A: Zero variance occurs when p=0 or p=1, meaning all outcomes are identical.

Q4: How does variance change with more trials?
A: Variance increases linearly with the number of trials (n).

Q5: Can this be used for non-binary outcomes?
A: No, this applies only to binary outcomes (success/failure) in independent trials.