5. Packet Failures (21 points) Consider three different models for sending n packets over the Internet: 1. each packet takes a different path. Each path fails independently with probability p; 2. all packets take the exact same path which fails with probability p. Thus, either all the packets get through or none get through; 3. half the packets take one path, and half take the other (assume n even), and each of the two paths fails independently with probability p. Let X,- be the number of packets lost in case i, for i = 1, 2, 3. Write down the probability mass function, the expectation of X,- and the variance of X,- for i : 1, 2, 3