What Is Bernoulli Distribution?
Table Of Contents:
- What Is Bernoulli Distribution?
- Formula For Bernoulli Distribution.
- Diagram For Bernoulli Distribution.
- Examples Of Bernoulli Distribution.
- What Is A Bernoulli Trail?
- Difference in Binomial and Bernoulli Distribution.
(1) What Is Bernoulli Distribution?
- Bernoulli Distribution applies to events that have one trial and two possible outcomes.
- Bernoulli Distribution is a discrete probability distribution, meaning it’s concerned with discrete random variables.
- A discrete random variable is one that has a finite or countable number of possible values—the number of heads you get when tossing three coins at once, or the number of students in a class.
(2) Formula For Bernoulli Distribution.
- P = Bernoulli Probability
- Here, ‘x’ is the outcome, which can either be a success (x=1), or failure, ( x=0)
- ‘p’ is the probability of getting success.
- q = 1-p, and it denoted the probability of failure.
- The value of p is 0 < p < 1.
(3) Diagram For Bernoulli Distribution.
- The graph shows that the probability of success is p when X = 1 and the probability of failure of X is (1 – p) or q if X = 0.
(4) Examples Of Bernoulli Distribution.
Example-1:Question
- A basketball player can shoot a ball into the basket with a probability of 0.6. What is the probability that he misses the shot?
Solution:
- We know that success probability P (X = 1) = p = 0.6
Thus, probability of failure is P (X = 0) = 1 – p = 1 – 0.6 = 0.4
Example-2: Questions
- Will you pass or fail a test?
- Will your favorite sports team win or lose their next match?
- Will you be accepted or rejected for that job you applied for?
- Will you roll a six in the opening round of your favorite board game?
- Will you win or lose the lottery?
- The probability of a roll of two dies resulting in a double six.
- How many boys are born and how many girls are born each day.
(5) What Is A Bernoulli Trail?
- A Bernoulli Trial is one of the simplest experiments you can conduct.
- It’s an experiment where you can have one of two possible outcomes.
- For example, “Yes” and “No” or “Heads” and “Tails.”
- It is named after Swiss mathematician Jacob Bernoulli,
Examples:
- Win or Loss of a cricket match.
- Boy or Girl child of a birth.
- Pass or Fail in an exam.
(6) Difference In Binomial and Bernoulli Distribution.
- In very simplistic terms, a Bernoulli Distribution is a type of Binomial Distribution.
- Bernoulli Distribution applies to events that have one trial and two possible outcomes. These are known as the Bernoulli trials.
- But in the case of a Binomial Distribution, we can have an ‘n’ number of trails.