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1.7 Let the random variable $X$ have the probability density function $f(x)=21?e_{??x?}x?(??,?)$ It is desired to quantize $X$ using the three level quantizer shown below. Let $Y$ denote the random variable at the output of the quantizer, i.e., $Y=?????101?X??1?1<X?1X>1?$ a) Find the conditional probability density function of $X$ conditioned on ${Y=?1}$, i.e., $f_{X}(x?Y=?1)$. b) Let $Q=Y?X$ be defined as the quantization error (or quantization noise). Find the conditional probability density function of the quantization error conditioned on ${Y=?1}$, i.e., $f_{Q}(q?Y=?1)$. c) Find the probability density function of $Q$.