DP Mathematics HL Questionbank
7.3
Description
[N/A]Directly related questions
- 18M.3sp.hl.TZ0.5b.ii: Hence write down an unbiased estimator of Var(X).
- 18M.3sp.hl.TZ0.5b.i: Show that \({\text{E}}\left( U \right) = \left( {n - 1} \right)p\left( {1 - p} \right)\).
- 18M.3sp.hl.TZ0.5a: Show that \(P = \frac{X}{n}\) is an unbiased estimator of \(p\).
- 16M.3sp.hl.TZ0.3c: (i) Show that \({\text{Var}}(U) = \frac{{{\theta ^2}}}{{6n}}\). (ii) Show that \({U^2}\)...
- 16M.3sp.hl.TZ0.3b: (i) Calculate an unbiased estimate for \(\theta \), using the random sample, 8.3, 4.2, 6.5,...
- 16M.3sp.hl.TZ0.3a: Find the value of \(k\).
- 17N.3sp.hl.TZ0.3b.iii: Hence find an expression for the most efficient estimator and interpret the result.
- 17N.3sp.hl.TZ0.3b.ii: Find, in terms of \({n_1}\) and \({n_2}\), an expression for \(a\) which gives the most efficient...
- 17N.3sp.hl.TZ0.3b.i: Show that...
- 17N.3sp.hl.TZ0.3a: Show that \(U = a{\bar X_1} + (1 - a){\bar X_2},{\text{ }}a \in \mathbb{R}\), is an unbiased...
- 17M.3sp.hl.TZ0.4c.ii: Hence find the variance of this best unbiased estimator.
- 17M.3sp.hl.TZ0.4c.i: Hence find the value of \(a\) and the value of \(b\) which give the best unbiased estimator of...
- 17M.3sp.hl.TZ0.4b: Show that \({\text{Var}}(U) = (39{b^2} - 12b + 1){\sigma ^2}\).
- 17M.3sp.hl.TZ0.4a: Given that \(U\) is unbiased, show that \(2a + 6b = 1\).
- 15N.3sp.hl.TZ0.5b: The die is rolled a second time, and the score \({X_2}\) is noted. (i) Show that...
- 15N.3sp.hl.TZ0.5a: (i) Find \({\text{E}}({X_1})\). (ii) Hence obtain an unbiased estimator for \(p\).
- 12M.3sp.hl.TZ0.1a: Determine unbiased estimates for the mean and variance of the distribution.
- 11M.3sp.hl.TZ0.3a: Determine unbiased estimates of the mean and variance of the loss in weight achieved over the...
- SPNone.3sp.hl.TZ0.1a: Determine unbiased estimates of \(\mu \) and \({\sigma ^2}\).
- 10N.2.hl.TZ0.2: The company Fresh Water produces one-litre bottles of mineral water. The company wants to...
- 13M.3sp.hl.TZ0.1a: Find unbiased estimates of \(\mu \) and \({\sigma ^2}\).
- SPNone.3sp.hl.TZ0.5b: In order to estimate \(\theta \), a random sample of n observations is obtained from the...
- 14M.3sp.hl.TZ0.3: (a) Consider the random variable \(X\) for which \({\text{E}}(X) = a\lambda + b\), where...
- 15M.3sp.hl.TZ0.2a: Determine unbiased estimates of \(\mu \) and \({\sigma ^2}\).
- 15M.3sp.hl.TZ0.4a: Explain briefly the meaning of (i) an estimator of \(\mu \); (ii) an unbiased estimator...
- 15M.3sp.hl.TZ0.4b: A random sample \({X_1},{\text{ }}{X_2},{\text{ }}{X_3}\) of three independent observations is...
- 14N.3sp.hl.TZ0.4c: Let \(T = \frac{Y}{2} + \frac{Y}{2}\). (i) Show that \(T\) is an unbiased estimator for...
Sub sections and their related questions
Unbiased estimators and estimates.
- 12M.3sp.hl.TZ0.1a: Determine unbiased estimates for the mean and variance of the distribution.
- 11M.3sp.hl.TZ0.3a: Determine unbiased estimates of the mean and variance of the loss in weight achieved over the...
- SPNone.3sp.hl.TZ0.1a: Determine unbiased estimates of \(\mu \) and \({\sigma ^2}\).
- SPNone.3sp.hl.TZ0.5b: In order to estimate \(\theta \), a random sample of n observations is obtained from the...
- 10N.2.hl.TZ0.2: The company Fresh Water produces one-litre bottles of mineral water. The company wants to...
- 13M.3sp.hl.TZ0.1a: Find unbiased estimates of \(\mu \) and \({\sigma ^2}\).
- 14M.3sp.hl.TZ0.3: (a) Consider the random variable \(X\) for which \({\text{E}}(X) = a\lambda + b\), where...
- 14N.3sp.hl.TZ0.4c: Let \(T = \frac{Y}{2} + \frac{Y}{2}\). (i) Show that \(T\) is an unbiased estimator for...
- 15M.3sp.hl.TZ0.4a: Explain briefly the meaning of (i) an estimator of \(\mu \); (ii) an unbiased estimator...
- 15M.3sp.hl.TZ0.4b: A random sample \({X_1},{\text{ }}{X_2},{\text{ }}{X_3}\) of three independent observations is...
- 15N.3sp.hl.TZ0.5a: (i) Find \({\text{E}}({X_1})\). (ii) Hence obtain an unbiased estimator for \(p\).
- 15N.3sp.hl.TZ0.5b: The die is rolled a second time, and the score \({X_2}\) is noted. (i) Show that...
- 18M.3sp.hl.TZ0.5a: Show that \(P = \frac{X}{n}\) is an unbiased estimator of \(p\).
- 18M.3sp.hl.TZ0.5b.i: Show that \({\text{E}}\left( U \right) = \left( {n - 1} \right)p\left( {1 - p} \right)\).
- 18M.3sp.hl.TZ0.5b.ii: Hence write down an unbiased estimator of Var(X).
Comparison of unbiased estimators based on variances.
- 14N.3sp.hl.TZ0.4c: Let \(T = \frac{Y}{2} + \frac{Y}{2}\). (i) Show that \(T\) is an unbiased estimator for...
- 15M.3sp.hl.TZ0.4b: A random sample \({X_1},{\text{ }}{X_2},{\text{ }}{X_3}\) of three independent observations is...
- 15N.3sp.hl.TZ0.5b: The die is rolled a second time, and the score \({X_2}\) is noted. (i) Show that...
- 18M.3sp.hl.TZ0.5a: Show that \(P = \frac{X}{n}\) is an unbiased estimator of \(p\).
- 18M.3sp.hl.TZ0.5b.i: Show that \({\text{E}}\left( U \right) = \left( {n - 1} \right)p\left( {1 - p} \right)\).
- 18M.3sp.hl.TZ0.5b.ii: Hence write down an unbiased estimator of Var(X).
\({\bar X}\) as an unbiased estimator for \(\mu \) .
- 15M.3sp.hl.TZ0.2a: Determine unbiased estimates of \(\mu \) and \({\sigma ^2}\).
- 18M.3sp.hl.TZ0.5a: Show that \(P = \frac{X}{n}\) is an unbiased estimator of \(p\).
- 18M.3sp.hl.TZ0.5b.i: Show that \({\text{E}}\left( U \right) = \left( {n - 1} \right)p\left( {1 - p} \right)\).
- 18M.3sp.hl.TZ0.5b.ii: Hence write down an unbiased estimator of Var(X).
\({S^2}\) as an unbiased estimator for \({\sigma ^2}\) .
- 15M.3sp.hl.TZ0.2a: Determine unbiased estimates of \(\mu \) and \({\sigma ^2}\).
- 18M.3sp.hl.TZ0.5a: Show that \(P = \frac{X}{n}\) is an unbiased estimator of \(p\).
- 18M.3sp.hl.TZ0.5b.i: Show that \({\text{E}}\left( U \right) = \left( {n - 1} \right)p\left( {1 - p} \right)\).
- 18M.3sp.hl.TZ0.5b.ii: Hence write down an unbiased estimator of Var(X).
