Many communication systems connecting computers employ a technique known as "packet transmission." In this type of system, a collection of binary digits (perhaps 1000 of them) are grouped together and transmitted as a "packet." The time interval between packets is a random variable that is usually assumed to be exponentially distributed with a mean value that is the reciprocal of the average number of packets per seconds that are transmitted. Under some conditions it is necessary for a user to delay transmission of a packet by a random amount that is uniformly distributed between 0 and T. if a user is generating 100 packets per second, and his maximum delay time, T , is 1 ms, find :
a) The probability density functions of the time interval between packets.
b) The mean value of the time interval between packets.