For the given analog source with probability density function $f_U(u),$ assume the entropy$-$coded quantizer is high$-$rate with a given large rate $R.$

$($a$)(5$ pts$)$Please determine which type of scalar quantizer is optimal.

$($b$)(5pts)$ Assume uin$(u_{\text{m}\text{i}\text{n}},u_{\text{m}\text{a}\text{x}}),$ describe how to design the quantization region size, quantization level and quantization points.

$($c$)(5$ pts$)$Give entropy of the quantizer.

$($d$)(5$ pts$)$Give MSE of the quantizer.