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In a data communication system, several messages that arrive at a node are bundled into a packet before they are transmitted over the network. Assume the messages arrive at the node according to a Poisson process with T= 26 messages per minute. Five messages are used to form a packet.

a) What is the mean time until a packet is formed, that is, until five messages arrived at the node?

b) What is the standard deviation of the time until a packet is formed?

c) What is the probability that a packet is formed in less than 10 seconds?

d) What is the probability that a packet is formed in less than 5 seconds?

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