Problem 1.8 (24 Points) Random variables X and Y are independent and are described by the probability density functions: fx(x) - 1, oxyx1 D, otherwise 0, otherwise Stations A and B are connected by two parallel meange channels, I and II. A mexiage from A to is sent over both channels at the same time. Random variables X and Y represent the meunge CSC/ECE 479 - AN 2022 delays (in hours) over parallel channels I and II, respectively. A message is considered "received" as soon as it arrives on any one channel, and it is considered "verified" as soon as it has arrived on both channels. (n) Determine the probability that a mesunge is received within 15 minutes after it is sent. (b) Determine the probability that the message is received but not verified within 15 minutes after it is sent. (e) Let I represent the time (in hours) between tromemission at A and verification at B. Deter- mine the CDF Fr(t), and then differentiate it to obtain the PDF fr(t). (d) If the attendant at If goes home 15 minutes after the menage is received, what is the prob- ability that he is present when the moonge should be verified ? (e) If the attendant at If leaves for a 15-minute coffee break right after the meunge is received, what is the probability that he is present at the proper time for verification ? (f) The management wishes to have the maximum probability of having the attendant present for both reception and verification. Would they do better to let him take his coffee break as described above, or simply allow him to go home 45 minutes after transmission