Question

Find the mean of a number randomly selected from 1 to 15.

Hint:

For uniform distribution over 1 to n, mean is \( \frac{n + 1}{2} \).

Answer 1

Numbers are 1, 2, ..., 15, with equal probability \( \frac{1}{15} \). Mean (expected value): \[ E(X) = \sum_{i=1}^{15} i \cdot \frac{1}{15} = \frac{1}{15} \cdot \frac{15 \cdot 16}{2} = \frac{120}{15} = 8. \] Alternatively, for a uniform distribution over \( \{1, 2, ..., n\} \), mean = \( \frac{n + 1}{2} = \frac{15 + 1}{2} = 8 \).
Answer: 8.