01 · Assignment Overview
Separate term values from totals and choose the right counting method for a small feature-selection system. Complete after Week 12.
Weeks 9–12
25
75–90 minutes
Instructions: Show the mathematical steps and explain each conclusion in one or two sentences. State any assumption you use. Hand reasoning and diagrams are required; Python or Colab may check a prediction but cannot replace the argument. Write your name and roll number on the first page.
Submission: One readable PDF of your own written or typed work, with pages in question order. Include diagrams and tables where requested. The instructor will announce the date and course-grade weight separately; the 25 points below describe only this assignment's internal rubric.
02 · Questions
Q1 · Sequence versus sum 5 points
A weekly activity log begins 4, 7, 10, 13, … entries.
- State the next two terms and a formula for aₙ with n starting at 1. (3)
- Find the total entries in the first six weeks, using a finite sum. Explain why the sixth term is not the total. (2)
Q2 · A recurrence model 5 points
A toy queue begins at b₁=2 and follows bₙ=2bₙ₋₁+1 for n≥2.
- Compute b₂,b₃,b₄,b₅, showing each substitution. (4)
- State one real-world limitation of treating this update rule as an accurate queue model. (1)
Q3 · Exploring possible feature sets 10 points
A team lists six distinct candidate features: A attendance, Q quiz result, S study hours, P practice count, T tutorial attendance, and R previous score. It plans a three-feature set. Assume all selections are allowed unless a restriction is explicitly stated.
- How many three-feature sets are possible? Explain why order does not matter. (3)
- If the team ranks first, second and third distinct features, how many ordered rankings are possible? (2)
- How many three-feature sets must include A? (2)
- How many three-feature sets do not contain both A and Q together? Count and justify the excluded sets. (3)
Q4 · Overlap and a guarantee 5 points
Among 24 students, 12 attended a mathematics workshop, 11 attended a Python workshop, and 4 attended both. In a separate group, 13 students have birth months among the 12 calendar months.
- How many attended at least one workshop? How many attended neither? Show the overlap adjustment. (3)
- What repetition is guaranteed in the separate birth-month group? Explain in one sentence. (2)
03 · Submission Checklist
- Distinguish a₆ from the sum through week 6.
- Show the initial value in every recurrence trace.
- For each feature count, justify whether order and restrictions matter.
- Explain overlap subtraction and the guarantee, not only the numbers.
Mark distribution: 5 + 5 + 10 + 5 = 25. Optional enumeration in Colab may verify a small answer after the hand count.