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 $b=1 / 24$