Chapter 1.2, Problem I.30E

A large building may require an automated alarm system which monitors and controls all fire and security alarms in the building. Normally, the building is divided into zones and a number of alarms are associated with each zone. Alarms alert a central manned control area who may pass these on to the emergency services or may respond personally.Factors which have to be taken into account in building such a system are:Ø If the control area is unmanned and an alarm is activated this alarm should not be ignored if it is potentially serious. Emergency services should be automatically called.Ø Some but not all parts of the building may be equipped with sprinkler systems or systems to shut down electrical equipment. These should be activated if a fire alarm is confirmed. They should not be activated if there are people in the same room.Ø The building may be equipped with direction indicators which illuminate the route to the nearest exit. These should be activated when a fire alarm is…

A robbery has just been committed at the Corner Market in the downtown area of the city (black rectangle in the city map). The market owner was able to activate the alarm, and the robber fled on foot. Police officers arrived a few minutes later and asked the owner, "How long ago did the robber leave?" "He left only a few minutes ago," the store owner responded. "He's probably ten blocks away by now", one of the officers said to the other. "Not likely," said the store owner. "He was so stoned on drugs that I bet even if he run ten blocks, he's still only within a few blocks of here! He's probably just running in circles!"Perform a simulation experiment that will test the store owner's hypothesis. Assume that at each corner of a city block there is an equal chance that the robber will go in any one of the four possible directions, north, south, east or west. Simulate for ten steps and five trials, and then indicate in how many of the trials the robber is within three blocks of the store.

Functions are used to map elements from one set to another. For example, barcode and QR scanner systems are developed by programmers to use specific symbologies to map the pattern in the barcode to actual digits. The check digit or the final digit is used to determine whether the function is true (known good) or false (errors in the mapping occurred). RFID system developers also use functions to develop a pairing protocol that securely connects legitimate devices within a specific proximity. RFIDs are using in logistics, retail, warehousing, and more.