Homework 6.2: More practice model building (15 pts)

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A former student in this class did an experiment where he had a collection of bacterial cells in a microfluidic chamber. The cells had fluorescently tagged mechnosensitive ion channels. Based on fluorescence, he could determine the number \(N\) of channels each cell had. He then exposed the cells to an osmotic shock and observed whether each cell exploded or survived the shock. So, for each cell he had a data pair, \((N, S)\), where \(S\) is one if the cell survived and zero if it exploded. Develop a generative model for this system.

There is a well-known class of models used to describe experiments like this. If you already know that this class of model is and you choose to use it, give justification as to why. If you do not know about this class of model, please do not try to figure out who the student is, look up his paper, etc. Instead, be creative! Think about how you would model this.