Conditional expectation calculator

This calculator accepts a finite list of possible values, the joint probability attached to each outcome, and a marker showing whether that outcome belongs to the conditioning event. It adds the probability mass inside the event, renormalizes those selected outcomes, and returns the resulting expected value. It also reports the intermediate probability and weighted sum, making the calculation easy to inspect or incorporate into a larger analysis.

Represent the joint outcomes and conditioning event

Enter one row for every possible joint outcome in the discrete model. The value field is the value taken by the random variable X, while probability is the probability mass assigned to that complete outcome. Set in_event to true exactly when the outcome belongs to the event A that you want to condition on. Repeated values are allowed because different underlying outcomes can produce the same value of X while differing in event membership or probability. The rows together must describe a complete probability distribution, so their probabilities must be nonnegative and sum to one. This explicit row format avoids ambiguity about whether a probability is marginal, conditional, or joint: every probability belongs to the outcome on its own row. Include zero-probability outcomes if they are useful for documenting the model, although they do not affect the result. Do not pre-normalize only the selected rows; provide the original joint probabilities so the calculator can determine P(A) and perform the conditioning correctly.

Understand how the conditional expectation is calculated

The calculator first adds the probabilities of all rows marked in_event, producing the conditioning probability P(A). It separately multiplies each selected value by its original joint probability and adds those products. The conditional expectation is the weighted selected sum divided by P(A): E[X given A] equals the sum of x times P(X equals x and A), divided by P(A). Dividing by the event probability renormalizes the selected probability mass so that it behaves like a complete distribution after the event is known. The response includes conditional_expectation, conditioning_probability, and weighted_event_sum, along with selected and total row counts. These intermediate fields are useful for auditing a result and catching modeling mistakes. If P(A) is zero, division would be undefined, so the capability returns an invalid-input error instead of producing Infinity, NaN, or a misleading numeric answer. All arithmetic is deterministic and uses the supplied finite numbers directly.

Check assumptions before using the result

A conditional mean is only as meaningful as the event and distribution supplied to it. Confirm that the rows are mutually exclusive and collectively exhaustive, since overlapping rows would double-count probability and missing rows would leave the distribution incomplete. The sum-to-one validation catches many omissions, but it cannot determine whether two semantic outcomes overlap. Also check that in_event expresses the information actually observed. Conditioning on a related but different event can produce a plausible number that answers the wrong question. For large or tiny values, review the returned weighted_event_sum and conditioning_probability as a quick numerical sanity check. A rare event can make the conditional expectation depend strongly on a small amount of probability mass; that sensitivity is mathematically valid, but the input probabilities may deserve extra scrutiny. For automated work, the same deterministic calculation is available through the API for $0.002 per request, allowing reproducible checks in risk models, quality-control pipelines, classroom tools, and decision analyses.