Free SOA Exam SRM (Statistics for Risk Modeling) Unsupervised Learning Techniques Practice Questions

Unsupervised learning on SOA Exam SRM covers principal component analysis (PCA), k-means and hierarchical clustering, and dimensionality reduction techniques for exploratory data analysis.

127 Questions
50 Easy
62 Medium
15 Hard
2026 Syllabus

Sample Questions

Question 1 Easy
In PCA, eigenvalues of the covariance matrix represent:
Solution
D is correct.

Each eigenvalue of the covariance (or correlation) matrix equals the variance of the data when projected onto the corresponding principal component. Larger eigenvalues indicate directions that capture more variation in the data.
Question 2 Medium
Which of the following statements about PCA is FALSE?
Solution
C is correct.

PCA is an unsupervised technique and does not require or use a response variable. It seeks directions of maximum variance in the feature space without regard to any outcome.
Question 3 Hard
K-means is applied to 6 one-dimensional observations with K=2K = 2. After convergence, cluster 1 contains {1,3,5}\{1, 3, 5\} and cluster 2 contains {9,11,13}\{9, 11, 13\}. What is the total within-cluster sum of squares (WCSS)?
Solution
A is correct.

Cluster 1: {1,3,5}\{1, 3, 5\}, centroid xˉ1=(1+3+5)/3=3.0\bar{x}_1 = (1+3+5)/3 = 3.0

Cluster 1 WCSS:
- (1−3)2=4(1-3)^2 = 4
- (3−3)2=0(3-3)^2 = 0
- (5−3)2=4(5-3)^2 = 4
- Sum = 4+0+4=8.04 + 0 + 4 = 8.0

Cluster 2: {9,11,13}\{9, 11, 13\}, centroid xˉ2=(9+11+13)/3=11.0\bar{x}_2 = (9+11+13)/3 = 11.0

Cluster 2 WCSS:
- (9−11)2=4(9-11)^2 = 4
- (11−11)2=0(11-11)^2 = 0
- (13−11)2=4(13-11)^2 = 4
- Sum = 4+0+4=8.04 + 0 + 4 = 8.0

Total WCSS =8.0+8.0=16.0= 8.0 + 8.0 = 16.0.
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