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Discrete Random Variables definitions

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  • Random Variable
    A symbol representing a value determined by chance in an experiment, with possible outcomes mapped to probabilities.
  • Discrete Random Variable
    A type with countable, distinct outcomes, such as dice rolls or number of prizes won in a raffle.
  • Continuous Random Variable
    A type with outcomes that can take any value within a range, allowing for infinite possible values, like heights.
  • Probability Distribution
    A table or function showing all possible outcomes of an experiment and their associated probabilities.
  • Outcome
    A possible result from an experiment, each paired with a probability in a probability distribution.
  • Probability
    A value between 0 and 1 assigned to an outcome, indicating its likelihood within a distribution.
  • Mean
    A weighted average of all possible values, calculated by summing each value times its probability.
  • Expected Value
    A long-run average outcome for a random variable, found by multiplying each value by its probability and summing.
  • Variance
    A measure of how spread out the outcomes are, found by subtracting the mean squared from the average of squared values.
  • Standard Deviation
    A measure of spread, equal to the square root of variance, indicating typical deviation from the mean.
  • Frequency Distribution
    A summary showing how often each value occurs in a dataset, often compared to probability distributions.
  • Experiment
    A process or action with uncertain outcomes, each outcome assigned a probability in a distribution.
  • Sigma Notation
    A mathematical symbol (∑) used to indicate summing values, such as in calculating means or variances.
  • Table
    An organized arrangement of outcomes and probabilities, aiding calculations for means and variances.
  • Decimal
    A numerical format commonly used for probabilities, ensuring values are between 0 and 1.