(Solved): 1.7 Let the random variable X have the probability density function f(x)=21exx( ...

1.7 Let the random variable $X$ have the probability density function $f(x)=\frac{1}{2}{e}^{??x?}x?(??,?)$ 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., $Y=?\begin{array}{ll}?1& X??1\\ 0& ?1<X?1\\ 1& X>1\end{array}$ 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 $Q$.