Variance of a Binomial Distribution Calculator
Calculates the variance of a binomial random variable X based on the number of trials and the probability of success.
Formula first
Overview
The variance represents the spread of the probability distribution around the mean. It is derived from the properties of independent Bernoulli trials, specifically the sum of variances of n independent Bernoulli variables. A higher variance indicates greater uncertainty in the outcome of the binomial experiment.
Symbols
Variables
n = Number of trials, p = Probability of success
Apply it well
When To Use
When to use: Use this when you need to quantify the dispersion of outcomes in a binomial experiment with a fixed number of trials and a constant probability of success.
Why it matters: It is essential in quality control and risk management for predicting the volatility or deviation from the expected average in binary outcomes.
Avoid these traps
Common Mistakes
- Confusing the variance with the standard deviation (which requires a square root).
- Using the wrong probability value, such as using the probability of failure instead of success.
One free problem
Practice Problem
A coin is tossed 20 times. Given the probability of landing heads is 0.5, calculate the variance of the number of heads.
Solve for: Var(X)
Hint: Use the formula np(1-p) where n=20 and p=0.5.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Ross, S. M. (2014). A First Course in Probability (9th ed.). Pearson.
- Cambridge International AS and A Level Mathematics: Probability & Statistics 1 Coursebook.
- A-Level Mathematics Specification: Statistics and Probability