Binomial Distribution
Definition
In statistics, a binomial distribution represents discrete data from repeated independent experiments with two possible outcomes (success or failure) and a fixed number of trials. It provides probabilities for each possible number of successes in those trials.
Analogy
Think about flipping a fair coin multiple times. A binomial distribution would help us calculate the probabilities of getting a certain number of heads (successes) out of those flips.
Related terms
Bernoulli Trial: A Bernoulli trial is an experiment with two possible outcomes, usually referred to as success and failure.
Probability Mass Function: The probability mass function (PMF) gives the probability that a discrete random variable takes on a specific value.
Expected Value: The expected value is the average outcome of a random variable over many trials. It represents the long-term average result.
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Practice Questions (13)
- In a binomial distribution, the probability of success for each trial is 0.3. What is the probability of failure for each trial?
- Which type of variable is used in binomial distribution?
- What is the binomial distribution formula, where n is the number of trials, x is the number of successes, and p is the probability of success?
- In a binomial distribution, the probability of success for each trial is 0.25. What is the probability of getting at least 2 successes in 5 independent trials?
- Which of the following conditions is necessary for using the binomial distribution to model a random event?
- Which condition is not required for using the binomial distribution to model a random event?
- Which of the following is a necessary condition for using the binomial distribution?
- In a binomial distribution, if the probability of success on each trial increases, what happens to the standard deviation?
- In a binomial distribution, what happens to the mean as the number of trials increases?
- If a random event does not meet one of the conditions for using the binomial distribution, what does it indicate?
- What must be true about the probability of success in order to use a binomial distribution?
- How should trials be conducted in order to use a binomial distribution?
- Which is a mnemonic device to help remember the conditions of a binomial distribution?
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