IS2.3

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Christian Lawson-Perfect

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Ready to use

10 years ago

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Christian Lawson-Perfect 10 years ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 10 years ago

Saved a checkpoint:

Removed a reference to the sketch of the PDF, because the image has gone missing.

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Bill Foster 12 years, 3 months ago

Created this.

Name	Status	Author	Last Modified
IS2.3	Ready to use	Bill Foster	01/06/2016 09:47
Alex's copy of IS2.3	draft	Alex Van den Hof	31/03/2017 11:40

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Question statement

Given the pdf

\[\begin{eqnarray*} f(x)&=&\simplify[std]{({f1}-{s1}x)/{n1}}\;\;\var{a} \leq x \leq \var{b}\\ f(x)&=&0\;\;\;\textrm{otherwise} \end{eqnarray*} \]
find the following probabilities:

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	0
f1	number	5
c	decimal	dec("1")
b	integer	4
d	decimal	dec("3")
f	integer	20
tol1	integer	0
m	integer	1
pd1	number	0.1250
n	integer	3
pc	number	0.6250
s	integer	2
r	integer	4
u	integer	91
t	integer	64
pd	number	0.20
tol	integer	0
n1	number	12
s1	number	1
gc	number	4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0..2)

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`

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap 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.

$P(X \gt \var{c})=\;\;$Unnamed gap

Input to 4 decimal places.

Advice

a)

We have:

\[\begin{eqnarray*} P(X \gt \var{c})&=&\int_{\var{c}}^{\var{b}}f(x)\;dx\\ &=&\frac{1}{\var{n1}}\int_{\var{c}}^{\var{b}}\simplify[std]{({f1}-{s1}x)}\;dx\\ &=&\frac{1}{\var{n1}}\left(\simplify[std,!otherNumbers]{{f1}({b}-{c})-{s1}({b}^2-{c}^2)/2}\right)\\ &=&\simplify[std]{{2*f1 * (b -c) + s1 * (c ^ 2 -(b ^ 2))} / {2*n1} }\\ &=& \var{pc} \end{eqnarray*} \] to 4 decimal places.

b)

\[\begin{eqnarray*} P(X \gt \var{d} | X \gt \var{c})&=&\frac{P(X \gt \var{d}\;\;\textrm{and}\;\; X \gt \var{c})}{P(X \gt \var{c})}\\ &=&\frac{P(X \gt \var{d})}{P(X \gt \var{c})} \end{eqnarray*} \] as $\var{d} \gt \var{c}$.

But,
\[\begin{eqnarray*} P(X \gt \var{d})&=&\int_{\var{d}}^{\var{b}}f(x)\;dx\\ &=&\frac{1}{\var{n1}}\int_{\var{d}}^{\var{b}}\simplify[std]{({f1}-{s1}x)}\;dx\\ &=&\frac{1}{\var{n1}}\left(\simplify[std,!otherNumbers]{{f1}({b}-{d})-{s1}({b}^2-{d}^2)/2}\right)\\ &=&\simplify[std]{{2*f1 * (b -d) + s1 * (d ^ 2 -(b ^ 2))} / {2*n1} }\\ &=& \var{pd1} \end{eqnarray*} \] to 4 decimal places.

Hence \[\begin{eqnarray*} P(X \gt \var{d} | X \gt \var{c})&=&\frac{P(X \gt \var{d})}{P(X \gt \var{c})}\\ &=&\frac{\var{pd1}}{\var{pc}}\\ &=&\var{pd} \end{eqnarray*} \] to 2 decimal places.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 10 years ago

Christian Lawson-Perfect 10 years ago

Bill Foster 12 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

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Error

IS2.3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 10 years ago

Christian Lawson-Perfect 10 years ago

Bill Foster 12 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

Generated value: `integer`