Exercise · ZW-ESTIMATOR-004 · ★☆☆ Basic
For a random sample with mean \(\mu\), which of these is an unbiased estimator of \(\mu\)?
Choose one option.
Show answer
- D. \(\bar X\)
Explanation
\(E[\bar X]=\mu\). The others have expectation \(\mu+1\), \(2\mu\) and \(2\mu\), so they are biased except for special values of \(\mu\).
Review the concept: Estimator
An estimator \(\hat\theta\) is a rule \(T\), a function of the random sample \(X_i\), that produces a value used to approximate an unknown population parameter \(\theta\).
\[\hat\theta=T(X_1,\dots,X_n)\]
More practice problems: estimator
- ZW-ESTIMATOR-001 With the sample 4,\ 8,\ 6,\ 10, bar X is used to estimate μ. What estimate is obtained?
- ZW-ESTIMATOR-002 Out of 50 patients, 18 respond to the treatment. If the sample proportion estimates p, what is the…
- ZW-ESTIMATOR-003 An estimator hatθ satisfies E[hatθ]=θ+2. What is its bias?
- ZW-ESTIMATOR-005 For the data 2,\ 4,\ 6,\ 8, what is the sample variance S^2 (dividing by n-1)?
- ZW-ESTIMATOR-006 An estimator has variance 4 and bias 1. What is its mean squared error?
- ZW-ESTIMATOR-007 A population has σ^2=36. With n=9, what is the variance of bar X?
- ZW-ESTIMATOR-008 With n=25, which unbiased estimator of μ is preferable: bar X or just X_1?
- ZW-ESTIMATOR-009 If μ=3 and hatμ=2bar X is used, what is the bias?