Class Note for STAT 427 at OSU
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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Ohio State University taught by a professor in Fall. Since its upload, it has received 16 views.
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Date Created: 02/06/15
Stat 427 Example of Unauthorized Entrance to a Secure Area Consider the situation where a bank ATM cash withdrawal security system involves keying in a valid K digit account number which if accepted is followed by electronic scanning and recognition of the customer s right thumb print In order for an unauthorized individual to fraudulently withdraw cash they would have to A guess a valid K digit ID number let PrID denote the probability of this event occurring B successfully pass the electronic thumb print scanning process let PTPdenote the probability of this event Assuming that these two events are independent then the probability of fraudulently withdrawing cash FW denoted by PFWwould be calculated as PFW PIDXPTP Calculation of PFW assuming K is known and N attempts are made to guess the ID Under the assumption that the individual knows the ID length K and walks away after they obtain a valid ID but fail to pass the thumb print scan the PFW can be calculated exactly as follows Let N be the number of attempts allowed by an unauthorized user to randomly select a valid ID of length K Consider the following sequence of mutually exclusive events A1 unauthorized user randomly selects a valid ID of length K on the first attempt A2 unauthorized user fails to select a valid ID on the first attempt and randomly selects a valid ID on the second attempt AN unauthorized user fails to select a valid ID on the first Nl attempts and successfully selects a valid ID on the Nth attempt The probability of successfully selecting a valid ID given N possible attempts is given by N PID 2 HA i1 Let CSID denote the event of correctly selecting a valid ID at random on a single attempt Let PCSID denote the probability of correctly selecting a valid ID at random on a single attempt Assuming sampling from the population of all possible ID s with replacement ie ignoring the negligible finite correction factor that would be required if the sampling was done without replacement then 1 fraudcashwdexampledoc M 10K PCSID where M is the number of valid ID s in the bank s database Let CSID denote the complimentary event of failing to select a valid ID at random on a single attempt then M PCSID 1 0K It follows that fori l 2 N M M P A 1 quot1 X 10K 10K Therefore N M N M i PIDZPA K ZIP K 1 i1 10 i1 10 The unconditional probability of fraudulent withdrawal is therefore given by PFWgt11lt Z1 N KHXPTP Notice that this equation involves two probabilities PID and PTP The probability PID involves three parameters M K and N which are known and in fact K can be set by bank management This probability equation can be used to perform sensitivity analyses to determine how sensitive PFW is to the values of M K and PTP This equation can be studied to determine the appropriate values for K to reduce the probability of fraudulent withdrawals to acceptable levels Figures 1 and 2 are examples of this type of analysis for the evaluation of the effect of the model parameters on PID 2 fraudcashwdexampledoc Scatterplot of PID vs K N123456789m 131 9 5 m m 300 m m C K 0 0 0 1 7 M 0 8 6 4 2 1 0 0 0 0 EU Scatterplot of PID vs K N12345678 11 9m u 3 10000 Customers M 10 08 fraudcashwdexampledoc
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