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An input to a $6$-level quantizer has the probability density function $f(x)$ as shown in the figure. Decision boundaries of the quantizer are chosen so as to maximize the entropy of the quantizer output. It is given that $3$ consecutive decision boundaries are $\text{‘-1’, ‘0’}$ and $\text{‘1’.}$
1. $\frac{152}{9}$
2. $\frac{64}{3}$
3. $\frac{76}{3}$
4. $28$