This chapter provides an overview of probability distributions in statistics. It begins by differentiating between discrete and continuous distributions, explaining how experiments with countable versus measurable outcomes are modelled. Discrete distributions are introduced with the probability mass function (PMF), while continuous distributions are with the probability density function (PDF). The Cumulative Distribution Function (CDF) is then presented as a tool for determining the probability that a random variable is less than or equal to a specific value. The chapter also touches on expectation and variance, explaining how these metrics summarise distribution characteristics. The widely used normal distribution is discussed in detail, including its mathematical properties and applications. The chapter also covers other important distributions like Bernoulli, Binomial, and Poisson, offering practical examples for each to illustrate their use in modelling real-world phenomena.

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Introduction to Distributions

  • Umberto Michelucci

摘要

This chapter provides an overview of probability distributions in statistics. It begins by differentiating between discrete and continuous distributions, explaining how experiments with countable versus measurable outcomes are modelled. Discrete distributions are introduced with the probability mass function (PMF), while continuous distributions are with the probability density function (PDF). The Cumulative Distribution Function (CDF) is then presented as a tool for determining the probability that a random variable is less than or equal to a specific value. The chapter also touches on expectation and variance, explaining how these metrics summarise distribution characteristics. The widely used normal distribution is discussed in detail, including its mathematical properties and applications. The chapter also covers other important distributions like Bernoulli, Binomial, and Poisson, offering practical examples for each to illustrate their use in modelling real-world phenomena.