Chapter 10: Continuous probability distributions Notes

Sections

1. 10A Cumulative frequency and probability Mastered

   Cumulative frequency and cumulative relative frequency, the cumulative distribution function of a discrete random variable, grouped continuous data, median and quartiles from a cumulative graph, and probability as area under a histogram.

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2. 10B Probability density functions Mastered

   Continuous random variables, probability density functions and their two conditions, probabilities as integrals, the cumulative distribution function and its relationship with the PDF, uniform distributions, piecewise PDFs, the median, and PDFs over unbounded domains.

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3. 10C Mean and variance of a continuous distribution Mastered

   The mean or expected value, variance and standard deviation of a continuous random variable found by integration, the uniform distribution, and linear changes aX + b.

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4. 10D The standard normal distribution Mastered

   The standard normal distribution with mean 0 and standard deviation 1, its bell-shaped PDF, finding probabilities with a table or calculator, symmetry, and quartiles.

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5. 10E The general normal distribution Mastered

   Normal distributions with any mean and standard deviation as shifted and stretched standard normals, z-scores, finding probabilities by standardising, comparing scores from different distributions, and working backwards from a probability.

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6. 10F The empirical rule Mastered

   The 68–95–99.7 empirical rule for normal distributions, finding percentages and predicting numbers of data values, identifying unusual values, and checking whether data is roughly normal.

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