3. A random sample \(X _ { 1 } , X _ { 2 } , \ldots X _ { n }\) is taken from a population with unknown mean \(\mu\) and unknown variance \(\sigma ^ { 2 }\). A statistic \(Y\) is based on this sample.
- Explain what you understand by the statistic \(Y\).
- Explain what you understand by the sampling distribution of \(Y\).
- State, giving a reason which of the following is not a statistic based on this sample.
- \(\sum _ { i = 1 } ^ { n } \frac { \left( X _ { i } - \bar { X } \right) ^ { 2 } } { n }\)
- \(\sum _ { i = 1 } ^ { n } \left( \frac { X _ { i } - \mu } { \sigma } \right) ^ { 2 }\)
- \(\sum _ { i = 1 } ^ { n } X _ { i } ^ { 2 }\)