1. **Stating the problem:** We are given a piecewise function $$R(\tau)$$ defined as: $$R(\tau) = \begin{cases} \lambda^2, & |\tau| > \lambda^2 \\ \lambda(1 - 3|\tau|), & |\tau| \leq 3 \end{cases}$$ 2. **Understanding the function:** This function has two parts depending on the value of the absolute value of $$\tau$$. - When $$|\tau| > \lambda^2$$, the function is constant at $$\lambda^2$$. - When $$|\tau| \leq 3$$, the function is linear in $$|\tau|$$ with slope $$-3\lambda$$ and intercept $$\lambda$$. 3. **Important notes:** - The problem as stated has a mismatch in the conditions: $$|\tau| > \lambda^2$$ and $$|\tau| \leq 3$$. For the function to be well-defined, these intervals should cover all $$\tau$$ or be consistent. - Assuming $$\lambda^2 \leq 3$$, the function is defined piecewise on $$|\tau| \leq 3$$ and $$|\tau| > \lambda^2$$. 4. **Summary:** The function is: $$ R(\tau) = \begin{cases} \lambda^2, & |\tau| > \lambda^2 \\ \lambda(1 - 3|\tau|), & |\tau| \leq 3 \end{cases} $$ This completes the interpretation of the function as given. No further simplification or evaluation is possible without specific values for $$\lambda$$ or $$\tau$$.