Following the lead of given example, design an optimum 2-bit quantizer for a signal whose samples follow a triangular PDF,
![](https://test.transtutors.com/qimg/450423dd-fb98-4a02-ac1b-9851ae6528ff.png)
(a) Find the four quantization levels
and the three boundary points, ![](https://test.transtutors.com/qimg/19ed9578-7cee-4141-b549-bf7046eba888.png)
(b) Find the mean-squared distortion, d .
(c) Find the signal-to-quantization-noise ratio in dB.
Example
An exponential random variable has a PDF given by
![](https://test.transtutors.com/qimg/e79defd2-8147-49ca-9d40-a5245a81382d.png)
(a) Find the mean and variance of X .
(b) Find the conditional mean and the conditional variance given that X > 1 .