A network forensic analyst is responsible for identifying worms, viruses, and infected nodes in the computer network. A new methodology for finding patterns in data that signify infections was investigated in IEEE Transactions on Information Forensics and Security (May, 2013). The method uses multiple filters to check strings of information. For this exercise, consider a data string of length 4 bytes (positions), where each byte is either a 0 or a 1 (e.g., 0010). Also, consider two possible strings, named S1 and S2. In a simple single-filter system, the probability that S1 and S2 differ in any one of the bytes is .5. Derive a formula for the probability that the two strings differ on exactly x of the 4 bytes. Do you recognize this probability distribution?