Probability and Statistics for Computer Scientists by Baron Michael;

Author:Baron, Michael;
Language: eng
Format: epub
Publisher: CRC Press LLC
Published: 2019-05-15T00:00:00+00:00

Definition 8.3

Sample mean is the arithmetic average,

Naturally, being the average of sampled observations, estimates the average value of the whole distribution of X. Computed from random data, does not necessarily equal μ; however, we would expect it to converge to μ when a large sample is collected.

Sample means possess a number of good properties. They are unbiased, consistent, and asymptotically Normal.

Remark: This is true if the population has finite mean and variance, which is the case for almost all the distributions in this book (see, however, Example 3.20 on p. 62).

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