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Geometric Distribution Formula:
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The Geometric Distribution is a probability distribution that models the number of independent Bernoulli trials needed to achieve the first success. It is used to calculate the probability of experiencing a certain number of failures before the first success occurs.
The calculator uses the Geometric Distribution formula:
Where:
Explanation: The formula calculates the probability of achieving the first success after exactly n-1 failures in a sequence of independent Bernoulli trials.
Details: The geometric distribution is widely used in reliability engineering, quality control, and risk assessment to model the number of trials until the first occurrence of an event. It helps in understanding the likelihood of success after a certain number of attempts.
Tips: Enter the probability of success (between 0 and 1), probability of failure (between 0 and 1), and the number of trials. All values must be valid (probabilities between 0-1, number of trials > 0).
Q1: What is the relationship between geometric and binomial distributions?
A: While binomial distribution counts successes in fixed trials, geometric distribution counts trials until first success.
Q2: What are the key assumptions of geometric distribution?
A: Independent trials, constant probability of success, and binary outcomes (success/failure).
Q3: How is geometric distribution used in real-world applications?
A: It's used in manufacturing (defect detection), sports (shot attempts until first goal), and marketing (customer conversions).
Q4: What is the expected value of geometric distribution?
A: The expected number of trials until first success is 1/p, where p is the probability of success.
Q5: Are there limitations to geometric distribution?
A: It assumes constant probability and independent trials, which may not hold in all real-world scenarios.