1. Consider a communication system with two transmitters and one receiver. Each millisecond, only one transmitter sends packets to the receiver. Transmitter 1 transmits packets with probability 0.6. Otherwise, transmitter 2 will transmit packets.

   Assume the numbers of packets sent by transmitter 1 and transmitter 2 in one millisecond are uniformly distributed in 0, 1, 2, 3, 4 and 0, 1, 2, 3, 4, 5, 6, respectively.

   Let X be the number of packets sent to the receiver in one millisecond.

   (a) Find the pmf of X.
   (b) Find the expected value of X. (c) Find the variance of X.