Problem 5 A message being sent over a communications network is assigned by a router to one of three paths (path 1, path 2, path 3). The nature of the network is such that 50% of all messages are routed to path 1, 30% are routed to path 2, and 20% are routed to path 3. If routed to path 1, then the message has a 75% chance of reaching its destination immediately. Otherwise, the message experiences a vesecond delay and returns to the router. If routed to path 2, then the message has a 60% chance of reaching its destination immediately. Otherwise, the message experiences a ten-second delay and returns to the router. If routed to path 3, then the message has a 40% chance of reaching its destination immediately. Otherwise, the message experiences a twentysecond delay and returns to the router. Note that the router cannot distinguish between new messages and messages that have returned from an unsuccessful attempt. Let X denote the time until the message reaches its destination. Determine E(X) and StDev(X)