FiniteProbabilitySpace

FiniteProbabilitySpace represents a finite sample space with an explicit probability mass function and provides the main finite conditional-expectation operations.

Constructor

FiniteProbabilitySpace(outcomes, probabilities)

Parameters

Properties

Methods

• probability(event) / probability_of(event) — probability of an event.
• random_variable(values, name=None) — create a RandomVariable on the space.
• partition(blocks) — create a validated Partition.
• conditional_probability_given_event(event, condition) — conditional probability given an event.
• conditional_expectation_given_event(random_variable, event) — conditional expectation given an event.
• conditional_expectation(random_variable, partition) — conditional expectation with respect to a partition.
• conditional_expectation_given(random_variable, condition) — conditional expectation under a supported finite conditioning object.
• conditional_probability(event, condition) — probability conditioned on a finite conditioning object.
• are_partitions_independent(first, second) — test independence of two partitions.
• are_independent(first, second) — test independence of supported random variables/partitions.
• conditional_characterization_error(random_variable, partition) — finite conditional-expectation characterization error.
• total_expectation(random_variable, partition) — law of total expectation.
• tower(random_variable, fine, coarse) — tower property.
• pull_out(multiplier, random_variable, partition) — pull-out property under the implemented finite conditions.
• conditional_variance(random_variable, partition) — conditional variance.
• conditional_covariance(first, second, partition) — conditional covariance.
• total_variance(random_variable, partition) — law of total variance.
• total_covariance(first, second, partition) — law of total covariance.
• l2_projection(random_variable, partition) — finite \(L^2\) projection on the conditioning partition.

Example

from stochx.stochastic import FiniteProbabilitySpace

space = FiniteProbabilitySpace(
    outcomes=["H", "T"],
    probabilities=[0.6, 0.4],
)
X = space.random_variable({"H": 1.0, "T": 0.0}, name="X")
print(space.probability_of({"H"}))
print(X.expected_value())

Related course material

Chapter 4 — Espérance conditionnelle