Problem 4: (15 Points) Source transmits data packets to a receiver. If received packet is error-free, receiver sends back ACK, otherwise it sends NAK. For each NAK, the packet is resent. Each packet transmission is independently received correctly with probability P 0.9. Please directly use the formulas to answer the following questions. 1. (2.5 points) Provide the average number of times a packet is transmitted i.e. E[X]). 2. (2.5 points) Provide the variance of X (i.e. var[X]). 3. (5 points. Each packet takes 2 msec to transmit. Source waits additional 1 msec to receive ACK or NAK. Let T equal the time required until the packet is received correctly. (a) (2.5 points) What is the relationship between X and T? (b) (2.5 points) Provide the variance of T. (i.e. var(71). 4. (5 points) If the packet transmission continues until the receiver correctly gets 4 packets. Let Z be the number of packets transmitted. (a) (2.5 points) Provide the average number of packets was transmitted (i.e. E[2]). (b) (2.5 points) Provide the variance of 2 (i.e. var[2])