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7: Distribution and Density Functions

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    • 7.1: Distribution and Density Functions
      This page covers various aspects of random variables and their probability distributions. It introduces random variables and distribution functions, explores diverse distributions like Bernoulli, Poisson, and normal, and provides mathematical details and examples of their applications. Key properties are highlighted, including the memoryless property of the exponential distribution and the significance of the normal distribution in the central limit theorem.
    • 7.2: Distribution Approximations
      This page covers the relationships between probability distributions, particularly how binomial and Poisson distributions approximate to Gaussian under certain conditions, alongside the significance of the central limit theorem. It also details the approximation of discrete distributions using simple random variables, discussing methods such as partitioning intervals and refining approximations for accuracy.
    • 7.3: Problems on Distribution and Density Functions
      This page contains exercises on random variables and probability distributions, including binomial, negative binomial, Poisson, exponential, gamma, and normal distributions. It emphasizes calculating probabilities and expected outcomes in various scenarios, such as store purchases, lamp failures, and customer arrivals. Key techniques include plotting distribution functions, using cumulative probabilities, and leveraging statistical functions and simulations.

    This page titled 7: Distribution and Density Functions was last modified on Sun, 25 Oct 2026 20:34:12 GMT and is shared under a CC BY 3.0 license and was authored, remixed, and/or curated by Paul Pfeiffer via source content that was edited to the style and standards of the LibreTexts platform.