3. Consider a training set that contains 100 positive examples and 400 negative examples. For each of the following candidate rules, R1: A −→ + (covers 4 positive and 1 negative examples), R2: B −→ + (covers 30 positive and 10 negative examples), R3: C −→ + (covers 100 positive and 90 negative examples), determine which is the best and worst candidate rule according to: (a) The likelihood ratio statistic.

None

Given a two-category classification problem under the univariate case, where there are two training sets (one for each category) as follows: D₁ = (-3,-1,0,4} D₂ = {-2,1,2,3,6,8} Given the test example x = 5, please answer the following questions: have and a) Assume that the likelihood function of each category has certain paramétric form. Specifically, we p(x | w₁) N, 07) p(x₂)~ N(μ₂, 02). Which category should we decide on when maximum-likelihood estimation is employed to make the prediction?

M3

2. Can you design a binary classification experiment with 100 total population (TP+TN+FP+ FN), with precision (TP/(TP+FP)) of 1/2, with sensitivity (TP/(TP+FN)) of 2/3, and specificity (TN/(FP+TN)) of 3/5? (Please consider the population to consist of 100 individuals.)

Generate test cases for the triangle problem by using the cause-effect graph and decision table testing

Question 1: Suppose that a Naive Bayesian classifier is created using a given training data set. Then, predictions are made on several testing points using this classifier. The predicted positive class probabilities and the actual class labels for these testing points are shown as follows. Please draw the ROC curve for the above prediction. Please clearly denote your splitting values and show the TP, FP, TN, FN, TPR, FPR values at each splitting value.   Sample ID Actual Class Label Predicted Positive Class Probability 1 - 0.1 2 + 0.3 3 - 0.4 4 + 0.4 5 + 0.6 6 + 0.8

Step 4: Hypothesis Test for the Population Mean (II) A team averaging 110 points is likely to do very well during the regular season. The coach of your team has hypothesized that your team scored at an average of less than 110 points in the years 2013-2015. Test this claim at a 1% level of significance. For this test, assume that the population standard deviation for relative skill level is unknown. You are to write this code block yourself. Use Step 3 to help you write this code block. Here is some information that will help you write this code block. Reach out to your instructor if you need help. 1. The dataframe for your team is called your_team_df. 2. The variable 'pts' represents the points scored by your team. 3. Calculate and print the mean points scored by your team during the years you picked. 4. Identify the mean score under the null hypothesis. You only have to identify this value and do not have to print it. (Hint: this is given in the problem statement) Assuming the…