Comprehensive Sampling Distribution Analysis

Parent Discrete Distribution

Values: [1, 2, 3, 4, 5]

Probabilities: [0.1, 0.2, 0.3, 0.2, 0.2]

Theoretical Mean: 3.3000

Theoretical Variance: 1.2400

Sample Size: 20

Mean of Sample Averages: 3.1946

Variance of Sample Averages: 0.0788

Relationship: Mean of the sample averages (3.1946) ≈ Parent mean (3.3000)

Relationship: Variance of the sample averages (0.0788) ≈ Parent variance / n (0.0780)

Sampling Distribution (n=20)

Sample Size: 30

Mean of Sample Averages: 3.1940

Variance of Sample Averages: 0.0518

Relationship: Mean of the sample averages (3.1940) ≈ Parent mean (3.3000)

Relationship: Variance of the sample averages (0.0518) ≈ Parent variance / n (0.0520)

Sampling Distribution (n=30)

Sample Size: 100

Mean of Sample Averages: 3.1950

Variance of Sample Averages: 0.0152

Relationship: Mean of the sample averages (3.1950) ≈ Parent mean (3.3000)

Relationship: Variance of the sample averages (0.0152) ≈ Parent variance / n (0.0156)

Sampling Distribution (n=100)