The quaternary constellation shown below is used to transmit over LAN cable. The information source is biased in the that $p(+3)=p(-3)=0\mathrm{.}35$ and $p(+1)=p(-1)=0\mathrm{.}15.$ It is corrupted by noise with variances, ${}_n^2=0\mathrm{.}25.$

a$.$ Solve for the average energy per symbol and per bit

b$.$ Using the maximum likelihood decision rule, what is the probability of bit error in terms of the Q function?

c$.$ With the given a priori probabilities, where should the boundaries be placed to minimize the bit error probability?