Expectation of a discrete random variable

The expectation is the probability-weighted average of all values a discrete random variable can take. It gives the long-run average value of the variable over many repeated trials.

E[X]=\sum_{x} x\,P(X=x)

What the symbols mean

discrete random variable
a possible value of X
probability that X takes the value x
expected value of X

About this formula

  • FieldStatistics
  • TopicProbability distributions
  • LevelHigh school
  • Also calledexpected value discrete random variable, mean of a discrete random variable, discrete expectation formula, probability weighted sum, expected value formula, mean value of discrete distribution

Write it in Obsidian

MathLive is a free visual math editor for Obsidian. Run Find a formula, type “expectation of a discrete random variable”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.

Related formulas