2012 2013 CBA3_2

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Bill Foster

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Ready to use

6 years, 4 months ago

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Bill Foster 6 years, 4 months ago

Gave some feedback: Ready to use

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Bill Foster commented 6 years, 4 months ago

Calculations are correct.

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Bill Foster 6 years, 4 months ago

Gave some feedback: Has some problems

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Bill Foster commented 6 years, 4 months ago

Should state in part c) that the answers are to be input to 2 decimal places.

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

Created this.

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Question statement

$X_1,\;X_2,\;\dots, X_n$ is a random sample from $\operatorname{Poisson}(\mu)$.

Let $\bar{x}$ denote the mean of this sample and for this exercise we have $n=\var{n},\; \bar{x}=\var{r11}$

Give any introductory information the student needs.

			Name	Type	Generated Value

r11	number	18.3
tulim	number	20.1655686226
per	integer	99
n	integer	35
mu	integer	18
tol	number	0.01
ulim	number	20.17
inf	number	1.91
z	number	2.58
llim	number	16.43
tllim	number	16.4344313774

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
precround(mean(repeat(poissonsample(mu),n)),1)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

18.3

← Depends on:

→ Used by:

inf
tllim
tulim

Statement
Advice
"Part a)" → "Unnamed gap" - Minimum accepted value
"Part a)" → "Unnamed gap" - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add
Part c) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Enter the m.l.e. $\hat{\mu}$ for $\mu$ here:

$\hat{\mu}=\;$?Unnamed gap

Advice

The maximum likelihood estimator (m.l.e) for $\mu$ is the sample mean i.e. $\hat{\mu}=\var{r11}$.

The expected information in this case is $\displaystyle \frac{n}{\bar{x}}$.

Hence $\displaystyle I(\mu)=\frac{\var{n}}{\var{r11}}=\var{inf}$ to 2 decimal places.

The $\var{per}$% confidence interval for $\mu$ in this case is given by $(a,b)$ where:

\[a=\bar{x}-z\sqrt{\frac{\bar{x}}{n}},\;\;b=\bar{x}+z\sqrt{\frac{\bar{x}}{n}},\;\;\;z=\var{z}\]

Calculating to 2 decimal places gives:

$a=\var{llim},\;\;\;b=\var{ulim}$.

Hence a $\var{per}$% confidence interval for $\mu$ is given by $(\var{llim},\var{ulim})$.

Give a worked solution to the whole question.

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Part	Test	Passed?
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Number entry
Number entry		Hasn't run yet
Gap-fill
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Number entry
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Gap-fill
Gap-fill		Hasn't run yet
Number entry
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Number entry
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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Bill Foster 6 years, 4 months ago

Bill Foster commented 6 years, 4 months ago

Bill Foster 6 years, 4 months ago

Bill Foster commented 6 years, 4 months ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

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2012 2013 CBA3_2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 4 months ago

Bill Foster commented 6 years, 4 months ago

Bill Foster 6 years, 4 months ago

Bill Foster commented 6 years, 4 months ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`