Discrete Probability Distributions

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What is a discrete probability distribution?

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A discrete probability distribution is a statistical distribution that describes the likelihood of a finite number of outcomes, where each outcome has a specific probability.

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What is the mean in a discrete probability distribution?

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The mean, or expected value, is the average of all possible values, each multiplied by its probability of occurrence.

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How do you calculate the probability of a specific number of events occurring in a Poisson distribution?

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The probability of k events occurring in a fixed interval is given by the formula: P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the average number of events.

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What is the significance of the sum of probabilities in a probability distribution?

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The sum of all probabilities in a probability distribution must equal 1, indicating that one of the possible outcomes must occur.

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What is the variance in a discrete probability distribution?

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Variance measures the spread of the distribution and is calculated as the average of the squared differences from the mean.

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What is the probability of getting more than a certain number of successes in a binomial distribution?

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To find the probability of getting more than k successes, you can use the complement rule: P(X > k) = 1 - P(X ≤ k).

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What is the difference between a binomial distribution and a Poisson distribution?

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A binomial distribution models the number of successes in a fixed number of trials, while a Poisson distribution models the number of events occurring in a fixed interval of time or space.

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What is the probability of exactly k successes in a binomial distribution?

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The probability of exactly k successes in n trials is given by the formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success.

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What does it mean for probabilities to be between 0 and 1?

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Probabilities must be between 0 and 1 inclusive, meaning that an event cannot have a negative probability and cannot exceed certainty.

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How do you interpret a probability of 0.1377 in a real-world context?

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A probability of 0.1377 means there is a 13.77% chance of the event occurring, which can be interpreted as approximately 1 in 7.25 chances.