• Syllabus

3.3

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Sub sections and their related questions

Unbiased estimators and estimates.

• 11M.1.hl.TZ0.1a: Bottles of iced tea are supposed to contain 500 ml. A random sample of 8 bottles was selected and...
• 10M.2.hl.TZ0.4a: The weights, \(X\) grams, of tomatoes may be assumed to be normally distributed with mean...
• 10M.2.hl.TZ0.4b: The random variable \(Y\) has variance \({\sigma ^2}\) , where \({\sigma ^2} > 0\) . A random...
• SPNone.2.hl.TZ0.2a: The farm manager selects a random sample of \(10\) apples and weighs them with the following...
• SPNone.2.hl.TZ0.7a: (i)     Find an expression for \(c\) in terms of \(n\) such that...
• SPNone.2.hl.TZ0.7b: (i)     Show that \({\rm{P}}(Y \le y) = {\left( {\frac{y}{a}} \right)^{3n}},0 \le y \le a\) and...
• SPNone.2.hl.TZ0.7c: Show that \(\frac{{{\rm{Var}}(U)}}{{{\rm{Var}}(V)}} = \frac{{3n + 2}}{5}\) and hence state, with...
• 14M.2.hl.TZ0.1: The random variable \(X\) has the binomial distribution \({\text{B}}(n,{\text{ }}p)\), where...
• 15M.2.hl.TZ0.2b: The sample values are summarized as \(\sum {x = 3782} \) and \(\sum {{x^2} = 155341} \) where...

Comparison of unbiased estimators based on variances.

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\(\overline X \) as an unbiased estimator for \(\mu \) .

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\({S^2}\) as an unbiased estimator for \({\sigma ^2}\) .

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