在某些情况下，可以使用 __________ 分布来近似与离散分布（如二项分布或泊松分布）相关的概率。

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The prompt asks: '在某些情况下，可以使用 __________ 分布来近似与离散分布（如二项分布或泊松分布）相关的概率。' This translates to: 'In some cases, a __________ distribution can be used to approximate probabilities related to discrete distributions such as the binomial or Poisson distribution.'

First, note that the provided answer_options are missing, which makes it impossible to analyze each option individually. In a typical multiple-choice setup, we would evaluate each candidate distribution and justify why it is or isn’t appropriate for approximating those discrete distributions.

However, drawing on standard statistical knowledge, the most common and appropriate fill-in is the 'Normal' distribution (also called the Gaussian distribution). The normal distribution is used to approximate the binomial distribution when the sample size n is large and the success probability p is not too close to 0 or 1, via the De Moivre–Laplace theorem, which underpins the normal approximation to the binomial. In practice, the binomial B(n, p) is approximated by N(np, np(1−p)) under suitable conditions, often with a continuity correction for better accuracy.

Regarding the Poisson distribution, a separate approximation scenario exists: when n is large and p is small (so that λ = np is moderate), the binomial distribution B(n, p) is well approximated by a Poisson(λ) distribution. Conversely, if we start from Poisson and want to approximate probabilities with a continuous model, the normal approximation can also be used under certain conditions for large λ, though the Poisson-to-normal route is less common for practical computation than the direct Poisson approximation to binomial.

The option labeled as '普通的' in the provided data appears to be a mistranslation or error. In Chinese, '普通的' means 'ordinary' or 'common' and is not the name of a probability distribution. This makes it an incorrect choice for filling the blank, since it does not denote a distribution type that could approximate binomial or Poisson probabilities.

If we were to flesh out hypothetical options, typical distinctions would be:
- Normal distribution: appropriate for normal approximation to binomial under large n and not-extreme p; sometimes used in broader approximations.
- Poisson distribution: typically used as an approximation to binomial for small p and large n, with λ = np.
- Other distributions (e.g., exponential, uniform) would generally be inappropriate for these particular approximations.

In summary, the standard correct fill-in is the Normal distribution for the common binomial normal approximation scenario, while the Poisson distribution serves as a separate, specific binomial approximation under the small-p regime. The provided '普通的' option does not correspond to a distribution name and is not appropriate as the fill-in for this question.

ECON 3640-090 2025 年春季讲座#16 热身

在某些情况下，可以使用 __________ 分布来近似与离散分布（如二项分布或泊松分布）相关的概率。

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ECON 3640-090 2025 年春季 讲座#16 热身

在某些情况下，可以使用 __________ 分布来近似与离散分布（如二项分布或泊松分布）相关的概率。

View Explanation

Log in for full answers

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Under which set of conditions is a binomial distribution approximated by a normal distribution?

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People born without creativity never can develop it

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ECON 3640-090 2025 年春季讲座#16 热身