List of formulas related to the variance of a discrete random variable:

  1. Definition of variance:
    [
    D(X) = \sum_{i=1}^{n} (x_i – \mu)^2 \cdot P(X = x_i)
    ]
    where (D(X)) is the variance of the random variable (X), (x_i) are the possible values ​​of (X), (\mu) is the mathematical expectation of (X), and (P(X = x_i)) is the probability that (X) will take the value (x_i).
  2. Mathematical expectation:
    [
    \mu = E(X) = \sum_{i=1}^{n} x_i \cdot P(X = x_i)
    ]
  3. An alternative formula for variance is:
    [
    D(X) = E(X^2) – (E(X))^2
    ]
    where (E(X^2) = \sum_{i=1}^{n} x_i^2 \cdot P(X = x_i)).

These formulas will help you calculate the variance of a discrete random variable.

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