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**Statement for Linked Answer Questions 82 & 83:**

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 $\text{‘1’.}$

The values of $a$ and $b$ are

- $a=1 / 6$ and $b=1 / 12$
- $a=1 / 5$ and $b=3 / 40$
- $a=1 / 4$ and $b=1 / 16$
- $a=1 / 3$ and $b=1 / 24$