| Exam Board | CAIE |
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| Module | FP2 (Further Pure Mathematics 2) |
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| Year | 2008 |
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| Session | November |
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| Topic | Linear combinations of normal random variables |
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| Type | Pooled variance estimation |
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6 The independent random variables \(X\) and \(Y\) have normal distributions with the same variance \(\sigma ^ { 2 }\). Samples of 5 observations of \(X\) and 10 observations of \(Y\) are made, and the results are summarised by \(\Sigma x = 15 , \Sigma x ^ { 2 } = 128 , \Sigma y = 36\) and \(\Sigma y ^ { 2 } = 980\). Find a pooled estimate of \(\sigma ^ { 2 }\).