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(This problem is based on Marchette and Wegman (2004, 13).) Cybersecurity is of major concern these days. It is rare the large institution that has not received a virus or is attacked on the internet. A network attack may occur by compromising multiple systems which are then used as platforms to mount a distributed attack. The victims send their responses to the spoofed addresses of the compromised system, not to the attacker. The compromised systems are chosen at random by the attacker. Assume that an attacker is selecting spoofed IP addresses from N total addresses. Further, assume that a network sensor monitors n IP addresses. The attacker sends k packets to the victim. A packet is the basic data part of the internet. (i) What is the probability of detecting an attack? What is the probability of seeing j packets?