Bhattacharyya Distance Between Two Distributions

Statistical Inference DS practice problem on Onlearn.

Difficulty: easy.

Topics: Understanding Bhattacharyya Distance Between Two Distributions, Bhattacharyya Coefficient, Discrete Probability Mass Function, Hellinger Distance, Floating Point Precision, Input Validation, Probability Theory, Information Theory, Statistical Inference, Numerical Analysis, Data Preprocessing, Probability Distributions, Distance Metrics, Measure Theory, Vector Operations, Error Handling.

Implement a function to calculate the Bhattacharyya distance between two probability distributions. The function should take two lists representing discrete probability distributions p and q, and return the Bhattacharyya distance rounded to 4 decimal places. If the inputs have different lengths or are empty, return 0.0.