IMPORTANT: If youre going to write please make sure your writing is neat and easy to read. Please write in print (not cursive).Please give a detailed explanation for your answers. Thank you

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A restaurant owner is considering opening a second location. She could potentially earn a $500k profit (net present value) if she opens the location and it is successful, but she stands to lose $100k (the fixed costs of setting up the new location) if it fails. She evaluates the prospects for the new location based on a vector of characteristics, X, which incudes location characteristics like foot traffic, availability of parking, proximity to public transportation, as well as characteristics of the surrounding population, average income, education, and demographic makeup. She makes a decision whether to open the new location based on whether the new location is predicted to succeed. There is available a dataset of n past restaurant location openings, and for each opening i the dataset records whether it succeeded, Yi, and the location and surround population characteristics, Zi. The goal is to classify restaurant openings as failures or successes based on characteristics x. Give the loss function the restaurant owner should use when training a model to predict success. Hint: the loss function's argument is the classification error, (;) Yi, where (xi) is predicted success (one for successful, zero for failure). Suppose now that instead of training a model to make a zero-one classification, you want to train a model to produce an estimate of the probability of success, p(xi). What loss function now is appropriate? Hint: now the loss function's argument is the prediction error, p(xi)-Yi; also, remember that the expectation of a binary variable is the probability that the variable is one. Suppose now that instead of training a model to make a zero-one classification, you want to train a model to produce an estimate of the probability of success, p(xi). What loss function now is appropriate? Hint: now the loss function's argument is the prediction error, p(xi)-Yi; also, remember that the expectation of a binary variable is the probability that the variable is one. A restaurant owner is considering opening a second location. She could potentially earn a $500k profit (net present value) if she opens the location and it is successful, but she stands to lose $100k (the fixed costs of setting up the new location) if it fails. She evaluates the prospects for the new location based on a vector of characteristics, X, which incudes location characteristics like foot traffic, availability of parking, proximity to public transportation, as well as characteristics of the surrounding population, average income, education, and demographic makeup. She makes a decision whether to open the new location based on whether the new location is predicted to succeed. There is available a dataset of n past restaurant location openings, and for each opening i the dataset records whether it succeeded, Yi, and the location and surround population characteristics, Zi. The goal is to classify restaurant openings as failures or successes based on characteristics x. Give the loss function the restaurant owner should use when training a model to predict success. Hint: the loss function's argument is the classification error, (;) Yi, where (xi) is predicted success (one for successful, zero for failure). Suppose now that instead of training a model to make a zero-one classification, you want to train a model to produce an estimate of the probability of success, p(xi). What loss function now is appropriate? Hint: now the loss function's argument is the prediction error, p(xi)-Yi; also, remember that the expectation of a binary variable is the probability that the variable is one. Suppose now that instead of training a model to make a zero-one classification, you want to train a model to produce an estimate of the probability of success, p(xi). What loss function now is appropriate? Hint: now the loss function's argument is the prediction error, p(xi)-Yi; also, remember that the expectation of a binary variable is the probability that the variable is one