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What is the sample space for the Negative Binomial Distribution?
What is the sample space for the Negative Binomial Distribution?
Which of the following best describes the Negative Binomial Distribution?
Which of the following best describes the Negative Binomial Distribution?
What does the random variable X represent in the Negative Binomial Distribution?
What does the random variable X represent in the Negative Binomial Distribution?
What is the probability of the event {X = x} for x ∈ {0, 1, 2, · · · } in the Negative Binomial Distribution?
What is the probability of the event {X = x} for x ∈ {0, 1, 2, · · · } in the Negative Binomial Distribution?
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What does the probability p represent in the Negative Binomial Distribution?
What does the probability p represent in the Negative Binomial Distribution?
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Study Notes
Sample Space of Negative Binomial Distribution
- The sample space consists of non-negative integers: {0, 1, 2, ...} representing the number of failures before achieving a specified number of successes.
Description of Negative Binomial Distribution
- The Negative Binomial Distribution models the number of failures in a sequence of Bernoulli trials before a predetermined number of successes occurs.
- It is a generalization of the geometric distribution, which focuses on the number of trials until the first success.
Random Variable X in Negative Binomial Distribution
- The random variable X represents the total number of failures encountered before achieving a specified number of successful trials (r).
Probability of Event {X = x}
- The probability mass function for the Negative Binomial Distribution is given by:
- P(X = x) = C(x + r - 1, r - 1) * p^r * (1 - p)^x
- Where C indicates the binomial coefficient, p is the probability of success on each trial, and x is the number of failures.
Probability p in Negative Binomial Distribution
- The probability p denotes the likelihood of success in each individual Bernoulli trial.
- It is a key parameter and influences the shape of the distribution.
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Description
Test your understanding of the Negative Binomial and Geometric distributions with this quiz. Explore the concepts of success probability and the number of trials needed for a certain number of successes.