Alex's copy of Is the given function a probability mass function?, , ,

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Alex Van den Hof 8 years ago

Created this as a copy of Is the given function a probability mass function?, , , .

Name	Status	Author	Last Modified
Is the given function a probability mass function?, , ,	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Alex's copy of Is the given function a probability mass function?, , ,	draft	Alex Van den Hof	31/03/2017 11:40

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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

is_pmf	boolean	false
has_negative_probability	integer	1
probabilities_dont_sum	integer	0
explain_decision	string	there is a negative probabilit

			Name	Type	Generated Value

a	integer	3
negerror	decimal	dec("-1")
c	number	67
b	integer	1
error	integer	0
d3	number	7
d4	number	12
d2	number	3
d1	number	-1

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Value

xxxxxxxxxx
 
has_negative_probability=0 and probabilities_dont_sum=0

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Generated value: `boolean`

false

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has_negative_probability
probabilities_dont_sum

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Does the following define a valid probability mass function?

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

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Advice

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

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

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

To verify this we calculate the function as follows:

$\begin{align} P(X = \var{d1}) &= \simplify[std]{({a} * {d1} + {b}) / {c} = {a * d1 + b} / {c}} \\ \\ P(X = \var{d2}) &= \simplify[std]{({a} * {d2} + {b}) / {c} = {a * d2 + b} / {c}} \\ \\ P(X = \var{d3}) &= \simplify[std]{({a} * {d3} + {b}) / {c} = {a * d3 + b} / {c}} \\ \\ P(X = \var{d4}) &= \simplify[std]{({a} * {d4} + {b}) / {c} = {a * d4 + b} / {c}} \end{align}$

and

$\sum_{x \in S} f(x) =\simplify[std]{ {a*d1+b}/{c} + {a*d2+b}/{c} + {a*d3+b}/{c} + {a*d4+b}/{c}} = \simplify[fractionNumbers]{{c-error}/{c}} = \simplify[std,simplifyFractions]{{c-error}/{c}}$

In this case, {if(is_pmf,"this is a probability mass function","this is not a probability mass function")} as {explain_decision}.

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Alex's copy of Is the given function a probability mass function?, , ,

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Alex Van den Hof 8 years ago

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Generated value: `boolean`

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Alex's copy of Is the given function a probability mass function?, , ,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Alex Van den Hof 8 years ago

Error in variable testing condition

Error

Warning

Generated value: boolean

Parts

Gap-fill

Generated value: `boolean`