The problem involves transforming a set of random variables $X_1, X_2, X_3$ (with given covariance matrix $C_X$) into a new set of random variables $Y_1, Y_2, Y_3$ using a transformation matrix $T$. You are asked to find the covariance matrix of the new random variables.

Given:

1. Covariance matrix $C_X$: 3.0 & 1.8 & 1.1 \\ 1.8 & 3.0 & 1.8 \\ 1.1 & 1.8 & 1.1 \end{bmatrix}$$
2. Transformation matrix $T$: 4 & -1 & -2 \\ 2 & 2 & 1 \\ -3 & -1 & 3 \end{bmatrix}$$

To Find:

The covariance matrix $C_Y$ of the new random variables $Y_1, Y_2, Y_3$, where: $C_Y = T C_X T^T$ where $T^T$ is the transpose of the transformation matrix $T$.

I'll now calculate the new covariance matrix $C_Y$.The covariance matrix $C_Y$ of the new random variables $Y_1, Y_2, Y_3$ is: