Clodagh's copy of Poisson Distribution (printing errors)

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Clodagh Carroll 8 years, 6 months ago

Published this.

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Clodagh Carroll 9 years, 1 month ago

Created this as a copy of Poisson Distribution (printing errors).

Name	Status	Author	Last Modified
Clodagh's copy of Poisson Distribution (printing errors)	draft	Clodagh Carroll	05/03/2021 12:07
Binomial Distribution (Cycling)	Ready to use	Julie Crowley	26/10/2023 12:21
Julie's copy of Clodagh's copy of Poisson Distribution (printing errors)	draft	Julie Crowley	07/03/2017 15:48
STAT7008 (Cycling)	draft	Catherine Palmer	06/10/2018 22:00
STAT7008 (printing errors)	Ready to use	Catherine Palmer	07/12/2021 15:12
Simon's copy of Binomial Distribution (Cycling)	draft	Simon Thomas	28/03/2019 12:17
Simon's copy of Clodagh's copy of Poisson Distribution (printing errors)	draft	Simon Thomas	28/03/2019 12:36
Simon's copy of Clodagh's copy of Poisson Distribution (printing errors)	draft	Simon Thomas	28/03/2019 14:36
Maria's copy of Binomial Distribution (Cycling)	draft	Maria Aneiros	27/05/2019 02:54
Exam07 - Binomial Distribution	draft	Michael Proudman	07/12/2021 09:54
nuExam07 - Binomial Distribution	draft	Michael Proudman	07/12/2021 09:54
Poisson Distribution (Dentist)	Ready to use	Catherine Palmer	22/03/2024 08:44
Binomial Distribution (Cycling)	Ready to use	Yvonne Wancke	26/06/2023 16:36
Binomial Distribution walks	Ready to use	Yvonne Wancke	26/06/2023 16:37
Poisson Distribution (Dentist)	Ready to use	Yvonne Wancke	26/06/2023 16:43
S2 EXAM Binomial Distribution 1	Ready to use	Yvonne Wancke	26/06/2023 16:34
S2 EXAM Poisson Distribution 1 doctors	Ready to use	Yvonne Wancke	26/06/2023 16:35

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Question statement

Please give your answer to at least 3 decimal places.

Printing errors in the work produced by a particular film occur randomly at an average rate of $\var{l}$ per page.

The Poisson distribution formula: $P(r)=\frac{\lambda^re^{-\lambda}}{r!}$ or $P(r)=e^{-\lambda}\left[\frac{\lambda^r}{r!}\right]$

Give any introductory information the student needs.

			Name	Type	Generated Value

l	number	0.25
x	integer	1
n	integer	11
y	integer	3
answer1	number	0.1947001958
answer2	number	0.4814567047
l2	number	2.75
pr0	number	0.0639278612
pr1	number	0.1758016183
pr2	number	0.2417272252

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0.05..0.4#0.1)

JME function reference

Description

average, lambda

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

Can an exam override the value of this variable?

Generated value: `number`

0.25

This variable doesn't seem to be used anywhere.

Advice

Part (a)

Remember that for a Poisson random variable:

$\begin{align} \operatorname{P}(X=x)&=\dfrac{\lambda^x\times e^{-\lambda}}{x!}\\ \end{align}$

$\begin{eqnarray*}\operatorname{P}(X = \var{x}) &=& \frac{\var{l} ^ {\var{x}}e ^ { -\var{l}}} {\var{x}!}\\& =& \var{answer1} \end{eqnarray*}$ to 3 decimal places.

Part (b)

2. For a $\var{n}$ page document, $\lambda=\var{n} \times \var{l} = \var{l2}$

The probability of having less than $\var{y}$ errors is given by:

$P(X < \var{y}) = P(X=0) + P(X=1) +P(X=2)$

where

$P(X=0) =\frac{\var{l2}^{0}e^{-\var{l2}}}{0!}=\var{pr0}$

$P(X=1) =\frac{\var{l2}^{1}e^{-\var{l2}}}{1!}=\var{pr1}$

$P(X=1) =\frac{\var{l2}^{2}e^{-\var{l2}}}{2!}=\var{pr2}$

Hence

$P(X < \var{y})$ = $\var{pr0}+\var{pr1}+\var{pr2}=\var{answer2}$

Give a worked solution to the whole question.

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Clodagh's copy of Poisson Distribution (printing errors)

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Taxonomy: mathcentre

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Clodagh Carroll 8 years, 6 months ago

Clodagh Carroll 9 years, 1 month ago

Error in variable testing condition

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Generated value: `number`

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Clodagh's copy of Poisson Distribution (printing errors)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Clodagh Carroll 8 years, 6 months ago

Clodagh Carroll 9 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Number entry

Advanced settings

Generated value: `number`