S2 June 2009 Q3

EdexcelOld spec5 marksDRVs

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.

(a) Explain what you understand by the statistic \(Y\). (2)
(b) Explain what you understand by the sampling distribution of \(Y\). (1)
(c) State, giving a reason which of the following is not a statistic based on this sample.

(i) \(\displaystyle\sum_{i=1}^{n}\dfrac{(X_i - \bar{X})^2}{n}\)      (ii) \(\displaystyle\sum_{i=1}^{n}\left(\dfrac{X_i - \mu}{\sigma}\right)^2\)      (iii) \(\displaystyle\sum_{i=1}^{n}X_i^2\)

(2)
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