[Solved] Question 4 (Non-existence of MLE for Logistic Regression ( -;;. We have data points {(x1, yı), …, (Xn, Yn)} with yi E {0,1}

Question 4 (Non-existence of MLE for Logistic Regression ( -;;. We have data points {(x1, yı), …, (Xn, Yn)} with yi E {0,1} from a pair of random variables (X,Y). We assume the data follows a logistic regression model Y|X = x ~ Bernoulli(n(x)), (0.1) eBх n(x) = (0.2) 14e8z Here, both B and X are scalars. (a) Write down the log-likelihood function for B. (b) Suppose the data turn out to be as follows. For every ti < 0 we have yi = 0. For every Xi > 0 we have Yi 1. Show that the maximum likelihood estimator B = 00. [This question shows you a strange behavior of logistic regression. When the data are perfectly separable, the MLE does not exist.]

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Answer to Question 4 (Non-existence of MLE for Logistic Regression ( -;;. We have data points {(x1, yı), …, (Xn, Yn)} with yi E {0,1}….