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Statistics LibreTexts

Supplemental Modules (Probability)

Probability theory is concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion.

  • Area Under the Normal Curve and the Binomial Distribution
    Typically the probability distribution does not follow the standard normal distribution, but does follow a general normal distribution. When this is the case, we compute the z-score first to convert it into a standard normal distribution
  • Probability and Independence
    For an experiment we define an event to be any collection of possible outcomes. A simple event is an event that consists of exactly one outcome. "or" means the union (i.e. either can occur) "and" means intersection (i.e. both must occur)
  • Probability Distributions
    A variable whose value depends upon a chance experiment is called a random variable. Suppose that a person is asked who that person is closest to: their mother or their father. The random variable of this experiment is the boolean variable whose possibilities are {Mother, Father}. A continuous random variable is a variable whose possible outcomes are part of a continuous data set.
  • The Central Limit Theorem
    Consider the distribution of rolling a die, which is uniform (flat) between 1 and 6. We will roll five dice we can compute the pdf of the mean. We will see that the distribution becomes more like a normal distribution. That is due to the Central Limit Theorem.
  • The Normal Distribution and Control Charts
    The Random Distribution is a special distribution that we will use often and is a distribution for a continuous random variable.
  • The z-score
    The number of standard deviations from the mean is called the z-score.
  • Tree Diagrams and Counting
    A tree diagram is a diagram that branches out and ends in leaves that correspond to the final variety.