What is the Difference Between Bernoulli and Binomial?
🆚 Go to Comparative Table 🆚The main difference between Bernoulli and Binomial distributions lies in the number of trials and the outcomes they represent.
- Bernoulli Distribution: This distribution deals with the outcome of a single trial of an event, with two possible outcomes: 0 or 1. It is used when the outcome of an event is required for only one time. For example, if you toss a coin with a 25% probability of heads, a single toss of the coin has a Bernoulli distribution, with p = 0.25.
- Binomial Distribution: This distribution deals with the outcome of multiple trials of a single event, where each trial has two possible outcomes: 0 or 1. It is used when the outcome of an event is required multiple times. In order for a random variable to follow a Binomial distribution, the probability of "success" in each Bernoulli trial must be equal and independent. For example, if you toss a coin 3 times and record the number of heads, this is now a Binomial distribution with p = 0.5 (probability of success on a given trial) and n = 3 (number of trials).
In summary:
- Bernoulli distribution represents the outcome of a single trial with two possible outcomes.
- Binomial distribution represents the outcome of multiple trials with two possible outcomes, where the probability of success in each trial is equal and independent.
On this pageWhat is the Difference Between Bernoulli and Binomial? Comparative Table: Bernoulli vs Binomial
Comparative Table: Bernoulli vs Binomial
Here is a table comparing the differences between Bernoulli and Binomial distributions:
Feature | Bernoulli Distribution | Binomial Distribution |
---|---|---|
Outcomes | Two possible outcomes: 0 or 1 | Multiple possible outcomes: 0, 1, 2, …, n |
Trials | Single trial | Multiple trials |
Success Probability | Set probability of success on a given trial | Probability of success on each trial is equal and independent |
Applications | Coin flip with fixed probability of heads | Coin flip experiment with multiple trials and different numbers of heads |
In summary, a Bernoulli distribution represents the outcome of a single trial with two possible outcomes, while a Binomial distribution represents the outcomes of multiple trials, each with the same probability of success, and multiple possible outcomes.
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