AI Math Competition: Bayesian Cohort Analysis Challenge
Grade 12 AI Literacy Competition
Competition Overview
This competition challenges Grade 12 students to apply Bayes' theorem and cohort analysis to solve realworld AI problems. Students will analyze a streaming service dataset to understand customer behavior
patterns and make data-driven predictions.
Learning Objectives
Apply Bayes' theorem to real-world scenarios
Understand cohort analysis in business contexts
Develop AI literacy through practical problem-solving
Practice mathematical reasoning with uncertainty
Problem Statement
Background
StreamLearn, an educational streaming service, wants to understand why students cancel their
subscriptions. As a data analyst, you must use Bayesian reasoning to analyze different student cohorts
and predict subscription renewal patterns.
Dataset Provided
Student Subscription Data (500 students)
Month_Joined | Student_ID | Age | Study_Hours_Week | Completed_Courses | Active_Months | Renewed
Jan_2024
| S001
| 16 | 12
|3
|8
| Yes
Jan_2024
Jan_2024
| S002
| S003
| 17 | 8
| 15 | 15
|1
|5
|4
| 12
| No
| Yes
Feb_2024
| S004
| 16 | 10
|2
|6
| Yes
Feb_2024
| S005
| 18 | 6
|1
|3
| No
Mar_2024
Mar_2024
| S006
| S007
| 17 | 14
| 15 | 11
|4
|3
|9
|7
| Yes
| Yes
Apr_2024
| S008
| 16 | 9
|2
|5
| No
Apr_2024
| S009
| 17 | 13
|4
|8
| Yes
May_2024
| S010
| 16 | 7
|1
|4
| No
Complete Dataset Summary (500 students):
January Cohort: 125 students (75 renewed, 50 did not renew)
February Cohort: 120 students (84 renewed, 36 did not renew)
March Cohort: 115 students (87 renewed, 28 did not renew)
April Cohort: 90 students (63 renewed, 27 did not renew)
May Cohort: 50 students (30 renewed, 20 did not renew)
Feature Definitions:
Month_Joined: Cohort identification (Jan-May 2024)
Age: Student age (15-18 years)
Study_Hours_Week: Weekly study time using the platform
Completed_Courses: Number of courses finished
Active_Months: Duration of active subscription
Renewed: Whether student renewed subscription (Yes/No)
Additional Data Insights:
Students with 10+ study hours/week: 70% renewal rate
Students with 5+ completed courses: 85% renewal rate
Students active for 6+ months: 80% renewal rate
Overall renewal rate: 68%
Competition Goals & Analysis Tasks
GOAL 1: Bayesian Probability Analysis (25 points)
Task A: Basic Bayes' Theorem Application
Calculate the probability that a student will renew their subscription given they study 12+ hours per
week.
Given Information:
P(Renew) = 0.68 (prior probability)
P(12+ hours/week | Renew) = 0.75
P(12+ hours/week | No Renew) = 0.30
P(12+ hours/week) = 0.55
Required:
1. Show the Bayes' theorem formula
2. Calculate P(Renew | 12+ hours/week)
3. Interpret the result in business context
Task B: Multi-Feature Bayesian Analysis
A new student joins with these characteristics:
Studies 14 hours/week
Completed 3 courses
Been active for 6 months
Calculate the probability of renewal using naive Bayes assumption.
GOAL 2: Cohort Analysis (30 points)
Task A: Cohort Performance Comparison
1. Calculate renewal rates for each monthly cohort
2. Identify the best and worst performing cohorts
3. Analyze trends across cohorts
Task B: Cohort Retention Analysis
Create a retention analysis showing:
Month 1-3: Early engagement patterns
Month 4-6: Mid-term retention
Month 7-12: Long-term loyalty
Calculate and compare retention rates across cohorts.
GOAL 3: Predictive Modeling (25 points)
Task A: Risk Assessment
Using Bayesian reasoning, classify students into risk categories:
High Risk (P(Renew) < 0.4): Likely to cancel
Medium Risk (0.4 ≤ P(Renew) < 0.7): Uncertain
Low Risk (P(Renew) ≥ 0.7): Likely to renew
Task B: Business Recommendations
Based on your analysis:
1. Which cohort needs immediate attention?
2. What student behaviors predict renewal?
3. Recommend 3 specific actions to improve retention
GOAL 4: AI Literacy Application (20 points)
Task A: Model Limitations
Explain 3 limitations of using Bayes' theorem for this problem:
1. What assumptions might be violated?
2. How could additional data improve predictions?
3. What biases might affect results?
Task B: Real-world AI Connection
Describe how this analysis relates to:
1. Machine learning recommendation systems
2. AI-powered customer segmentation
3. Automated decision-making in business
Submission Requirements
Mathematical Work (60%)
Calculations: Show all work for Bayesian computations
Formulas: Properly written mathematical expressions
Interpretations: Clear explanations of numerical results
Analysis & Insights (40%)
Data Understanding: Demonstrate comprehension of dataset
Pattern Recognition: Identify meaningful trends in cohorts
Business Context: Connect math to real-world applications
Format Requirements
Length: 8-12 pages (handwritten or typed)
Sections: Clearly labeled responses to each goal
Graphs/Charts: Visual representations of key findings
Citations: Reference any external sources used
Judging Rubric
Mathematical Accuracy (30 points)
Bayesian Calculations (15 points)
Excellent (13-15): Perfect application of Bayes' theorem with correct calculations and clear formula
presentations
Good (10-12): Mostly correct calculations with minor computational errors
Satisfactory (7-9): Basic understanding demonstrated with some calculation mistakes
Needs Improvement (0-6): Significant errors in Bayesian reasoning or calculations
Statistical Analysis (15 points)
Excellent (13-15): Accurate cohort analysis with proper statistical interpretations
Good (10-12): Good statistical work with minor interpretation issues
Satisfactory (7-9): Basic statistical analysis with limited depth
Needs Improvement (0-6): Poor statistical reasoning or major errors
Problem-Solving & Reasoning (25 points)
Analytical Thinking (15 points)
Excellent (13-15): Deep insights with creative problem-solving approaches
Good (10-12): Good analytical skills with solid reasoning
Satisfactory (7-9): Basic analysis with limited insight
Needs Improvement (0-6): Poor analytical approach or reasoning
Data Interpretation (10 points)
Excellent (9-10): Excellent interpretation of patterns and trends
Good (7-8): Good understanding of data implications
Satisfactory (5-6): Basic data interpretation
Needs Improvement (0-4): Poor or incorrect interpretations
AI Literacy & Application (25 points)
Understanding of AI Concepts (15 points)
Excellent (13-15): Clear understanding of AI/ML connections with thoughtful limitations discussion
Good (10-12): Good grasp of AI concepts with some limitations awareness
Satisfactory (7-9): Basic understanding of AI applications
Needs Improvement (0-6): Limited understanding of AI concepts
Real-world Connections (10 points)
Excellent (9-10): Excellent connections between math and real-world AI applications
Good (7-8): Good real-world connections
Satisfactory (5-6): Basic connections made
Needs Improvement (0-4): Poor or missing real-world connections
Communication & Presentation (20 points)
Clarity of Explanation (10 points)
Excellent (9-10): Clear, well-organized explanations that are easy to follow
Good (7-8): Generally clear with minor organization issues
Satisfactory (5-6): Basic clarity with some confusing sections
Needs Improvement (0-4): Poor organization or unclear explanations
Visual Presentation (10 points)
Excellent (9-10): Professional presentation with effective charts/graphs
Good (7-8): Good visual elements with minor presentation issues
Satisfactory (5-6): Basic visual presentation
Needs Improvement (0-4): Poor or missing visual elements
Competition Timeline & Prizes
Important Dates
Registration Deadline: [Date]
Competition Period: 2 weeks
Submission Deadline: [Date]
Results Announcement: 1 week after submission
Prizes
1st Place: $500 + AI summer camp scholarship
2nd Place: $300 + AI certification course
3rd Place: $200 + AI learning resources
Participation: Certificate of completion
Support Resources
Office Hours: Weekly online sessions with math teachers
AI Literacy Guide: Provided reference materials
Peer Discussion: Moderated online forum
Calculator Policy: Scientific calculators allowed, no programming calculators
Submission Method
Submit via school portal or email to competition organizers with:
Student name and school
Complete mathematical work
Signed honor code statement