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Random Variables

In probability and statistics, arandom variable, random quantity, aleatory variable, orstochastic variable is a variable whose possible values are outcomes of a random phenomenon.As a function, a random variable is required to be measurable, which rules out certain pathological cases where the quantity which the random variable returns is infinitely sensitive to small changes in the outcome. A random variable is defined as a function that maps the outcomes of unpredictable processes to numerical quantities (labels), typically real numbers. In this sense, it is a procedure for assigning a numerical quantity to each physical outcome. Contrary to its name, this procedure itself is neither random nor variable. Rather, the underlying process providing the input to this procedure yields random (possibly non-numerical) output that the procedure maps to a real-numbered value. A random variable has a probability distribution, which specifies the probability that its value falls in any given interval.

Random variables​

  1. Discrete random variables

  2. Continuous random variables

  3. Transforming random variables

  4. Combining random variables5. Binomial random variables

Binomial mean and standard deviation formulas

  1. Geometric random variables

Types of random variables​

  1. Discrete random variable

    • Taking any of a specified finite or countable list of values, endowed with a probability mass function characteristic of the random variable's probability distribution.
    • Can be infinite but countable meaning integers
    • Example
      • Toss a coin
      • Year that a student was born (infinite but countable)
      • Number of ants born tomorrow in the universe
      • Winning time in men's 100 meter dash in 2016 olympics rounded up to nearest hundreds

  2. Continuous random variable

    • Taking any numerical value in an interval or collection of intervals, via a probability density function that is characteristic of the random variable's probability distribution.
    • Should be real valued since more and more can be added in between two values
    • Example
      • Exact mass of a random animal selected a district zoo
      • Exact winning time in men's 100 meter dash in 2016 olympics

  3. Mixture of discrete and continuous random variable Two random variables with the same probability distribution can still differ in terms of their associations with, or independence from, other random variables. The realizations of a random variable, that is, the results of randomly choosing values according to the variable's probability distribution function, are called random variates.

https://en.wikipedia.org/wiki/Random_variable