Chapter 5 - Discrete Probability Distributions - 5-2 Mean, Variance, Standard Deviation, and Expectation - Exercises 5-2 - Page 272: 8

Mean = 3.441

Let's calculate the mean (expected value) step by step for this Benford's law distribution. Mean = μ = ∑X * P(X) =(1*0.301)+(2*0.176)+(3*0.125)+(4*0.097)+(5*0.079)+(6*0.067)+(7*0.058)+(8*0.051)+(9*0.046) = 3.441 This shows that smaller digits (like 1, 2, 3) occur more frequently in real-world data, which is why the mean is lower than 5 (the uniform case).