## [solution]: Explain the factors that influence one's eating behavior.

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1. Behavioural Authentication. Alice usually forgets to lock her cellphone, so she has developed an application for her cellphone that locks it if a finger swipe of the user does not match Alice?s finger swipe pattern.1 The classifier she is using for her application has a false acceptance rate(FAR)of 15% (i.e., the phone incorrectly identifies a stranger?s finger swipes as Alice?s swipes 15% of the time). The false rejection rate (FRR) of the classifier is 20% (i.e., the phone incorrectly

(This technology is called implicit authentication, and is currently an active topic of research.)

identifies Alice?s swipes as a stranger?s swipes 20% of the time). Being rejected frequently and not satisfied by the security of her application, Alice decides to modify it such that FAR and FRR decrease to less than 1% and 2%, respectively. So she adds a window of n swipes. Any swipe rejected by the classifier increases the rejection counter by one, and the counter is set to zero every six swipes if the phone is not already locked. Her application locks the cellphone as soon as the rejection counter reaches a threshold.

Find the smallest possible length of swipes for the window and a suitable threshold. Show calculations or the code you have used to compute your results (No need to prove the mini- mality of window size).

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