Which of the following DAG structures becomes MORE biased, not less, if you control for the middle variable?

Which linkage criterion merges the pair of clusters whose combination causes the smallest increase in within-cluster variance?

Using momentum with beta = 0.9 and velocity v initialized to 0, suppose the gradient is 2 at step 1 and 4 at step 2. What is the velocity v after step 2?

Lloyd’s algorithm for K-means alternates an assign step and an update step. What quantity does every iteration monotonically decrease (or leave unchanged)?

Use the graph of the function given below.  If the limit is infinite, write  or .  If the limit does not exist and is not infinite, write DNE. Use the math editor (“Insert Math Equation” as needed on the toolbar) to enter your final answer. Show all work on your paper.                                                                                          What type of discontinuity is at x = 2?                    

Use the graph of the function given below.  If the limit is infinite, write or .  If the limit does not exist and is not infinite, write DNE. Use the math editor (“Insert Math Equation” as needed on the toolbar) to enter your final answer. Show all work on your paper.                                                                                          Find .            

Evaluate the limit using algebraic or trigonometric methods when applicable. If the limit is infinite, write  or .  If the limit does not exist and is not infinite, write DNE. Use the math editor (“Insert Math Equation” as needed on the toolbar) to enter your final answer. Show all work on your paper. Find  using algebraic methods.

Evaluate the limit using algebraic or trigonometric methods when applicable. If the limit is infinite, write ∞ or −∞.  If the limit does not exist and is not infinite, write DNE. Use the math editor (“Insert Math Equation” as needed on the toolbar) to enter your final answer. Show all work on your paper. Find   using algebraic methods.

True or false: Mastery assignments are included to scaffold your efforts toward accomplishing the three major writing assignments successfully.

True or false: ChatGPT or other AI writing programs are considered a form of academic dishonesty. Use of these tools on any assignment will result in automatic failure of the assignment and may be reported to the Honor Code Office.