Suppose you are given the following set of data with three Boolean input variables a, b, c, and a single Boolean output variable K. Equation Equation Equation Equation 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 According to the naïve Bayes classifier, what is Equation? Note: Assume we are using a naïve Bayes classifier to predict the value of K from the values of the other variables. a. 0 b. 1/2 c. 1 Note: Max credits will only be received if you develop the expression of the probability.

How do SVMs handle the case of non-linearly separable data? (5 points) 

A product analytics team at a software company constructs a 95% confidence interval for the proportion of users who complete onboarding. Their current sample of n=400 users yields p^=0.55 and produces a total interval width of approximately 0.098. The team’s director wants to reduce this width to exactly half — approximately 0.049 — while keeping the confidence level fixed at 95%. Which of the following correctly identifies the required sample size change AND correctly explains why that specific change achieves the goal of halving the width?

Consider the three linearly separable two-dimensional input vectors in the following figure. Find the linear SVM that optimally separates the classes by maximizing the margin. The three points are (1,1.5), (0.5,1) and (1, 0.5). (10 points)  Hint: show and write the decision boundary and show the margin hyperplane H+ and H-.  

Once a weak classifier is picked in a particular round, it will never be chosen in any subsequent round.

A customer experience director at a subscription-based software company surveys 100 randomly selected current subscribers. The survey finds that 90 out of 100 customers (p^=0.90) report they would recommend the platform to a colleague. Using the Stats Kingdom calculator configured as a two-tailed proportion z-test with α=0.01, the output produces a 99% confidence interval of [0.8227, 0.9773] and a critical value of z*=2.5758. The director presents the following five conclusions about this confidence interval to the executive team. Select all statements that are TRUE.

A cloud computing company’s server response times follow a normal distribution with mean μ=200 ms and standard deviation σ=40 ms. The engineering team evaluates the following five statements about this distribution. Select all that are TRUE.

Below are the three scatter plots (A, B, C left to right) and hand drawn decision boundaries for logistic regression. Which of the above figure shows that the decision boundary is overfitting the training data? Please choose one choice and state your rationale. (5 points) a. A b. B c. C d. None of these

A hospital infection control officer investigates whether hand-hygiene compliance rates differ between the intensive care unit (ICU) and the general medical ward (GMW). Group 1 (ICU): n1=120, f1=85, p^1=0.7083. Group 2 (GMW): n2=85, f2=50, p^2=0.5882. A two-tailed two-sample proportions z-test at α=0.10 returns pooled proportion p^=0.6585, standard error =0.067226, test statistic z=1.7865, p-value =0.0740, critical value zcv=1.6452, and CI90=(0.009497,0.230699). Which of the following correctly identifies the statistical decision, the correct comparison that supports it, and the proper interpretation of the confidence interval result?

A market research firm tests whether the proportion of online shoppers who prefer subscription-based purchasing models differs from 50% (H0:p=0.50, H1:p≠0.50). A random sample of n=1,000 online consumers finds that 650 prefer subscription models (p^=0.65). Using a two-tailed proportion z-test at α=0.05, the Stats Kingdom calculator returns a test statistic of z=9.4868, critical values of ±1.9600, and a p-value of 0.0000. Which of the following correctly states both the comparison that leads to the statistical decision AND the conclusion that properly follows from it?