IP3.2

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Bill Foster

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Christian Lawson-Perfect

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9 years, 11 months ago

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Christian Lawson-Perfect 9 years, 11 months ago

Gave some feedback: Ready to use

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Bill Foster 12 years, 2 months ago

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Question statement

Determine whether the following defines a valid probability mass function.

Also choose the options which describe the function.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	2
negerror	decimal	dec("-1")
c	number	20
b	integer	-1
error	integer	0
flse2	string	All probabilities are non-nega
flse1	string	Probabilities do not sum to $1
d3	number	4
d4	number	8
u	integer	1
t	integer	0
correct1	string	Probabilities sum to $1$
correct2	string	There is a negative probabilit
flse	string	Yes, it is a probability mass
d2	number	1
correct	string	No, it is not a probability ma
d1	number	-1

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..4)

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:

c
negerror

Advice
"Part a)" - prompt

Parts

Part a) Gap-fill
1. Gap Choose one from a list
  Add
Part b) Gap-fill
1. Gap Choose several from a list
  Add

Gap-fill

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

Does the following define a valid probability mass function?

\[P(X=x) = \simplify{({a}x+{b})/{c}},\;\;\;x \in S=\{\var{d1},\;\var{d2},\;\var{d3},\;\var{d4}\}\]

Unnamed gap

Advice

A probability mass function $f(x)=P(X=x)$ has to satisfy:

1. $\sum_{x \in S} f(x) = 1$

2. $f(x) \ge 0,\;\;\forall x \in S$

In this case:

{correct} as

1. {correct1}

2. {correct2}

To verify this we calculate the function as follows:

\[ \begin{eqnarray*} P(X = \var{d1}) &=&\simplify[std]{({a} * {d1} + {b}) / {c} = {(a * d1 + b)} / {c}}\\ P(X = \var{d2}) &=&\simplify[std]{({a} * {d2} + {b}) / {c} = {a * d2 + b} / {c}}\\ P(X = \var{d3}) &=&\simplify[std]{({a} * {d3} + {b}) / {c} = {a * d3 + b} / {c}}\\ P(X = \var{d4}) &=&\simplify[std]{({a} * {d4} + {b}) / {c} = {a * d4 + b} / {c}} \end{eqnarray*} \]
and
\[\sum_{x \in S} f(x) =\simplify[std]{{c-error}/{c}}\]

as you can easily check.

Give a worked solution to the whole question.

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Choose several from a list
Choose several from a list		Hasn't run yet

This question is used in the following exams:

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Feedback

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Checkpoint description

Christian Lawson-Perfect 9 years, 11 months ago

Bill Foster 12 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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IP3.2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 9 years, 11 months ago

Bill Foster 12 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`