Expected Value of a Discrete Distribution

The expected value is the long-run average of a random variable — each outcome weighted by how often it happens:

Task: write expected_value(values, probabilities) returning E[X], rounded to 4 decimal places.

• The two lists line up by position: values[i] occurs with probability probabilities[i].
• The probabilities are guaranteed to sum to 1.

Worth noticing that the expected value need not be an outcome you can ever observe. A fair die averages 3.5, a number that isn't on any face — it describes the distribution, not any single roll.