20122013 CBA0_2

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Bill Foster

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6 years, 5 months ago

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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 that the three independent random variables $X_1,\;X_2,\;X_3$ have the following distributions:

{table(rs,[' ','Mean','Variance'])}

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	2
c	integer	8
b	integer	5
d	integer	9
rs	list	Nested 3×3 list
ex	integer	67
var	number	269

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-9..9 except [0,1,-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: `integer`

This variable doesn't seem to be used anywhere.

Parts

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.

Find the expectation and variance of:

$Y=\simplify[basic]{{a}*X_1+{b}*X_2+{c}*X_3+{d}}$

$\operatorname{E}[Y]=\;$ Gap 0.

$\operatorname{Var}(Y)=\;$ Gap 1.

Advice

If $Y=aX_1+bX_2+cX_3+d$ is a linear combination of independent random variables where $X_i$ has mean $m_i$ and variance $v_i,\;i=1,\;2,\;3$ then

$\operatorname{E}[Y]=am_1+bm_2+cm_3+d$ and $\operatorname{Var}(Y)=a^2v_1+b^2v_2+c^2v_3$

For this example we have:

$\operatorname{E}[Y]=\simplify[basic]{{a}*{rs[0][1]}+{b}*{rs[1][1]}+{c}*{rs[2][1]}+{d}}=\var{ex}$ and

$\operatorname{Var}(Y)=\simplify[basic]{{a^2}*{rs[0][2]}+{b^2}*{rs[1][2]}+{c^2}*{rs[2][2]}}=\var{var}$ .

Give a worked solution to the whole question.

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There was an error which means the tests can't run:

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

This question is used in the following exams:

Statistical inference by Newcastle University Mathematics and Statistics in Content created by Newcastle University.
exam toets by Gretel Crafford in Gretel's workspace.
Ann's copy of Statistical inference by Ann Smith in Ann's workspace.
Ann's copy of Ann's copy of Statistical inference by Ann Smith in Probability and Statistics.
Term 2-Test 1 by samira Al-Moustafa in samira's workspace.
CL2603StatsWeek1 by Ben Parker in Ben's workspace.
MA5636 Week2 by Ben Parker in Ben's workspace.
Long Test by Anne-Sophie Kaloghiros in MA1670.

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Taxonomy: mathcentre

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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

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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20122013 CBA0_2

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: integer

Parts

Gap-fill

Generated value: `integer`