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3: Distributions of Random Variables

  • 3.1: Normal Distribution
    Among all the distributions we see in practice, one is overwhelmingly the most common. The symmetric, unimodal, bell curve is ubiquitous throughout statistics. Indeed it is so common, that people often know it as the normal curve or normal distribution.
  • 3.2: Evaluating the Normal Approximation
    Many processes can be well approximated by the normal distribution. While using a normal model can be extremely convenient and helpful, it is important to remember normality is always an approximation. Testing the appropriateness of the normal assumption is a key step in many data analyses.
  • 3.3: Geometric Distribution (Special Topic)
    How long should we expect to flip a coin until it turns up heads? Or how many times should we expect to roll a die until we get a 1? These questions can be answered using the geometric distribution. We first formalize each trial - such as a single coin flip or die toss - using the Bernoulli distribution, and then we combine these with our tools from probability to construct the geometric distribution.
  • 3.4: Binomial Distribution (Special Topic)
    The binomial distribution describes the probability of having exactly k successes in n independent Bernoulli trials with probability of a success p.
  • 3.5: More Discrete Distributions (Special Topic)
    The "Negative binomial distribution" and "Poisson distribution" are discussed in this section.
  • 3.E: Distributions of Random Variables (Exercises)
    Exercises for Chapter 3 of the "OpenIntro Statistics" textmap by Diez, Barr and Çetinkaya-Rundel.


David M Diez (Google/YouTube), Christopher D Barr (Harvard School of Public Health), Mine Çetinkaya-Rundel (Duke University)