20122013 CBA1_1

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Bill Foster 6 years, 6 months ago

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Newcastle University Mathematics and Statistics 9 years, 4 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	0.0028
ans2	number	-5.873
ans3	decimal	dec("2.000")
m	number	2.5
tol4	number	0.0001
p	list	List of 3 items
v	matrix	matrix([0,2,4])
x2	integer	4
x0	integer	0
x1	integer	2

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Name

Data type

Value

xxxxxxxxxx
 
0.001

JME function reference

Description

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

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Generated value: `number`

0.001

This variable doesn't seem to be used anywhere.

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
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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.

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Taxonomy: mathcentre

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Bill Foster 6 years, 6 months ago

Newcastle University Mathematics and Statistics 9 years, 4 months ago

Error in variable testing condition

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Generated value: `number`

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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, 6 months ago

Newcastle University Mathematics and Statistics 9 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`