20122013 CBA1_1

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Bill Foster 6 years, 5 months ago

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Question statement

Suppose $\underline{x}=\var{v}$ is a vector of observations from a $\operatorname{Poisson}(\mu)$ distribution.

Give any introductory information the student needs.

			Name	Type	Generated Value

tol3	number	0.001
ans1	number	0.0001
ans2	number	-8.816
ans3	decimal	dec("3.000")
m	number	1.5
tol4	number	0.0001
p	list	List of 3 items
v	matrix	matrix([5,0,4])
x2	integer	4
x0	integer	5
x1	integer	0

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
0.001

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`

0.001

→ Used by:

"Part a)" → "Gap 1." - Minimum accepted value
"Part a)" → "Gap 1." - Maximum accepted value
"Part b)" → "Unnamed gap" - Minimum accepted value
"Part b)" → "Unnamed gap" - Maximum accepted value

Parts

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

Gap-fill

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

For $\mu=\var{m}$ calculate:

(i) $L(\mu,\underline{x})=\;$ ? Gap 0. (enter your answer to 4 decimal places).

(ii) $l(\mu,\underline{x})=\;$ ? Gap 1. (enter your answer to 3 decimal places).

Advice

a) If there are 3 observations from $\operatorname{Poisson}(\mu),\;(x_1,x_2,x_3)$ then:

(i)

$\operatorname{L}(\mu|\underline{x})=\frac{e^{-\mu}\mu^{x_1}}{x_1!}\times\frac{e^{-\mu}\mu^{x_2}}{x_2!}\times \frac{e^{-\mu}\mu^{x_3}}{x_3!}$

For this calculation $\mu=\var{m}$ and $(x_1,x_2,x_3)=\var{v}$ and we obtain:

$\operatorname{L}(\mu|\underline{x})=\var{p[0]}\times\var{p[1]}\times \var{p[2]}=\var{ans1}$ to 4 decimal places.

(ii)

$\operatorname{l}(\mu|\underline{x})=\ln(\operatorname{L}(\mu|\underline{x}))=\ln(\var{p[0]}\times\var{p[1]}\times \var{p[2]})=\var{ans2}$

to 3 decimal places.

b) The MLE is the mean of the observations i.e.

$\frac{\var{x0}+\var{x1}+\var{x2}}{3} = \var{ans3}$ to 3 decimal places.

Give a worked solution to the whole question.

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

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Taxonomy: mathcentre

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Taxonomy: Context

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Checkpoint description

Bill Foster 6 years, 5 months ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `number`

Parts

Gap-fill

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20122013 CBA1_1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 5 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`