A binary communication system makes use of the symbols “zero” and “one”. There are channel errors. Consider the following events:
$\begin{array}{ll} x_{0}& : & \text{a “zero” is transmitted} \\ x_{1} & : & \text{a “one” is transmitted} \\ y_{0} & : & \text{a “zero” is received} \\y_{1} & : & \text{a “one”is received} \end{array}$
The following probabilities are given $P\left ( x_{0} \right )=\frac{1}{2}, P\left ( y_{0}|x_{0} \right )=\frac{3}{4},$ $and$ $P\left ( y_{0} \mid x_{1}\right )=\frac{1}{2}.$ The information in bits that you obtain when you learn which symbol has been received (while you know that a “zero” has been transmitted) is _________
