List of top Engineering Mathematics Questions on Statistics asked in GATE XE

Let \(X\) and \(Y\) be two random variables with mean \(0\), variance \(1\), and correlation coefficient \(\tfrac{1}{3}\). Then the value of \(\mathrm{Var}(X+3Y)\) is equal to:

Let $A$ be a $3 \times 3$ real matrix having eigenvalues $1,2,3$. If \[ B = A^2 + 2A + I, \] where $I$ is the $3 \times 3$ identity matrix, then the eigenvalues of $B$ are: