Question 2: Q function and BPSK Modulation (20 points)
For BSPK modulation, bits are transmitted in $X = \pm \sqrt{E_b}$ and the receiver will get their corrupted versions with Gaussian noise, $Y = X + N$, where N is zero mean Gaussian random variable (R.V.) with a variance of $\sigma^2$.
1. Find the probabilities illustrated by the two colored areas in green and red in the figure below, respectively.
2. Explain what the meanings of the probabilities are.
3. What are bit error rate (BER) of QPSK modulation, according to the above sub questions.
4. What is the value of z that minimizes the BER of QPSK modulation.
