List of formulas related to the variance of a discrete random variable:
- 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). - Mathematical expectation:
[
\mu = E(X) = \sum_{i=1}^{n} x_i \cdot P(X = x_i)
] - 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.