$($a$)$ A receiver receives binary data at $9600$ bits per second as $+5$ mV for $1$ and $-5$ mV for $0.$ Find the $($i$)$ probability of error in reception when the data is corrupted with AWGN of two sided PSD of ${10}^{-9}$Wat$\frac{t}{H}z.$

$($ii$)$ percentage increase in error rate if data rate is doubled.

$($iii$)$ input voltage levels to keep the probability of error same as $($i$)$ with the increased data rate i$.$e$.$ doubled data rate.