A data packet is transmitted over a lossy wireless channel with packet error rate 0.3. Most communication systems adopt the Automatic Repeat reQuest (ARQ) protocol. That is, if a packet is successfully (with probability 0.7) or unsuccessfully (with probability 0.3) received, the receiver respectively sends a one-bit ACK' or NAK' message (over a separate feedback channel) to the transmitter. After receiving an ACK, the transmitter will move on to the next packet transmission; otherwise, the transmitter will re- transmit the same packet, and this process continues until the transmitter receives an ACK' message. (a) [2 points] Assume the feedback channel is reliable, let X denote the total number of transmissions (including re-transmission) for one packet, calculate P(X=3) and the expectation of X. (b) [1 points] Assume the feedback channel is reliable, given the first transmission fails, re-calculate the expectation of X. (c) [2 points] Assume the feedback channel is unreliable so that the NAK/ACK feedback bit flips with probability 0.2 (i.e., with 20% of chance the transmitter receives incorrect feedback). In this case, derive the Probability Mass Function (PMF) of X