Covariance from Joint Probability Mass Function
Probability Theory DS practice problem on Onlearn.
Difficulty: medium.
Topics: Understanding Covariance in Discrete Bivariate Distributions, Expectation E[X], Joint Expectation E[XY], Covariance Formula, Summation over Discrete Support, Floating Point Precision, Probability Theory, Statistics, Linear Algebra, Discrete Mathematics, Data Analysis, Joint Probability Distributions, Marginal Distributions, Expectation Operators, Moments of Random Variables, Linearity of Expectation.
Given a joint probability mass function (PMF) represented as a dictionary where keys are tuples (x, y) and values are probabilities, write a function to calculate the covariance Cov(X, Y). The function should return the covariance as a float.