Postdoc @ CHOP/PENN

This is the job application at Children's Hospital of Philadelphia and University of Pennsylvania. You can see the original post here: https://docs.google.com/document/d/1vBXrn0j2exfg715ppTMGoyN5-NlK_XP5GRjVZj_95nQ
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Please answer the following questions by recording your voice (maximum of 2 minutes each). You do not need to answer all of them, please answer as many as you can.

Audio recordings should be as simple as possible, please do not refer to any equations, plots, images, etc. Just plain English. If you like to change your response, simply re-record, and it will automatically overwrite the previous recording.
Let’s assume you have a prior understanding for the occurrence of an event (e.g., the probability of obtaining a head in a coin toss). Through experience in life and some systematic analysis, you collect some data about the event (e.g., you toss the coin n times and observe k heads). How would you update your prior understanding after seeing the data?
Suppose we are training a linear classifier and like to regularize parameter vector (w) using a penalty term. When would you use L1 penalty or L2 penalty?
Suppose we have a full-rank square matrix A and two vectors b and c. Also suppose that the difference (e.g., L2 norm) between b and c is very small. Suppose that the solution to Ax=b is x1 and the solution to Ax=c is x2. Turns out that the difference between x1 and x2 is very large. Can you describe why this may have happened?
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