Final answer:
To solve the mathematical question, calculate the variance and covariance by summing the weighted squared deviations and product of deviations for the paired outcomes, respectively, and then compute the variance of the sum of X and Y.
Step-by-step explanation:
The given question asks for the computation of various statistical measures based on a joint probability density function, such as variance, standard deviation, and covariance. To find the variance (σ²) of a discrete probability distribution, we need to calculate the sum of squared deviations of each outcome of the random variable from its mean, weighted by their respective probabilities. For the covariance between two random variables X and Y, Cov(X,Y), we need to look at the product of the deviations of each pair of outcomes from their respective means, again weighted by their probabilities. The variance of the sum of two random variables, Var(X + Y), can be computed using the formula Var(X + Y) = Var(X) + Var(Y) + 2Cov(X,Y).