Answer: 0

## Explanation Recall from the properties of the covariance that: $$ \text{Cov}(A, B + C) = \text{Cov}(A, B) + \text{Cov}(A, C) $$ So, we need: $$ \text{Cov}(X, K) = \text{Cov}(X, Y + Z) = \text{Cov}(X, Y) + \text{Cov}(X, Z) = 0 + 0 = 0 $$ This is true because X is independent of both Y and Z, which means: - Cov(X, Y) = 0 - Cov(X, Z) = 0 The correlation between Y and Z (ρ = 0.8) and the variances (σ² = 2) are irrelevant for calculating Cov(X, K) since X is independent of both Y and Z. Therefore, the covariance between X and K is 0.

Author: Tanishq Prabhu