Unformatted text preview: timator or estimate of μ. estimate ˆ ( µ is read as μ-hat.) n Example 1: To estimate the mean weight (μ) of the of seven million residents of Hong Kong, a sample of size 8 is taken. The results (in kg) are as follows: The 71.2, 60.0, 55.3, 65.4, 32.7, 78.6, 68.8, 59.6 Estimate μ. Estimate Solution: From the 8 data we can obtain easily, ˆ µ = x = 61.45 Note:
ˆ µ = x = 61.45 The estimate , computed according to (1) uses all the information in the sample fairly. There is no inbuilt intention to overestimate or underestimate μ. It is called an unbiased estimate for μ. unbiased To appreciate this, suppose we adopt a rule of dropping he largest value and using the average of the remaining data as an estimate for μ. ˆ Then, say, for the above data, µ = 71.2 + 60 + 55.3 + 65.4 + 32.7 + 68.8 + 59.6 = 59 Then, ˆ...
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- Spring '10
- Standard Deviation, Estimation theory, unbiased estimate