Past exam of the mathematical and Computational Biology course of the University of Cambridge / 2025 / Paper 1 / 3 / c / Solution

The total variance is the trace $\mathrm{tr}\Sigma =10$. Retaining two original genes preserves the sum of their marginal variances; the largest choice includes the third gene and either of the first two, giving $4+3=7$. Thus the largest proportion is 70%. This refers to retaining measured coordinates themselves, rather than replacing them by linear combinations as in principal component analysis.