Probability, expectation and standard deviation of Poisson distribution

Error

There was an error loading the page.

Contributors

History

○

Simon Thomas 6 years, 2 months ago

Created this.

Name	Status	Author	Last Modified
Probability, expectation and standard deviation of Poisson distribution	draft	Simon Thomas	07/02/2019 10:25
Brad's copy of Probability, expectation and standard deviation of Poisson distribution	draft	Brad Allison	18/06/2019 14:54

Question statement

{pre} $\var{thismany}$ .

{something} $\var{number1}$ {else}

Give any introductory information the student needs.

			Name	Type	Generated Value

pre	string	The mean number of sales per d
what	string	daily sales.
this	string	a randomly selected employee m
things	string	sales.
number1	integer	3
descx	string	the number of sales per day
else	string	per day.
thismany	integer	10
something	string	Employees receive a warning if
tol	number	0.001
v	integer	1
tprob1	number	0.063055458
sd	number	3.162
tprob2	number	0.0027693957
prob2	number	0.003
thisnumber	integer	6
thisaswell	string	a randomly selected employee r
prob1	number	0.063

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
"The mean number of sales per day at a telecommunications centre is "

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: `string`

The mean number of sales per day at a telecommunications centre is

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
Part b) 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.

Assuming a Poisson distribution for $X$ , {descX}, write down the value of $\lambda$ .

$X \sim \operatorname{Poisson}(\lambda)$

$\lambda =$ ?Gap 0.

Find $\operatorname{E}[X]$ the expected {descX}.

$\operatorname{E}[X]=$ ?Gap 1.

Find the standard deviation for {what}.

Standard deviation = ? Gap 2. (to 3 decimal places).

Advice

1. $X \sim \operatorname{Poisson}(\var{thismany})$ , so $\lambda = \var{thismany}$ .

2. The expectation is given by $\operatorname{E}[X]=\lambda=\var{thismany}$

3. $\operatorname{stdev}(X)=\sqrt{\lambda}=\sqrt{\var{thismany}}=\var{sd}$ to 3 decimal places.

$\begin{eqnarray*}\operatorname{P}(X = \var{thisnumber}) &=& \frac{e ^ { -\var{thismany}}\var{thismany} ^ {\var{thisnumber}}} {\var{thisnumber}!}\\& =& \var{prob1} \end{eqnarray*}$ to 3 decimal places.

2. If an employee receives a warning then he or she must have sold less than {number1}.

Hence we need to find :

$\begin{eqnarray*}\operatorname{P}(X < \var{number1})& =& \simplify[all,!collectNumbers]{P(X = 0) + P(X = 1) + {v}*P(X = 2)}\\& =& \simplify[all,!collectNumbers]{e ^ { -thismany} + {thismany} * e ^ { -thismany} + {v} * (({thismany} ^ 2 * e ^ { -thismany}) / 2)} \\&=& \var{prob2} \end{eqnarray*}$

to 3 decimal places.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

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
Number entry
Number entry		Hasn't run yet
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 not used in any exams.

Loading...

Error

Probability, expectation and standard deviation of Poisson distribution

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `string`

Parts

Gap-fill

Loading...

Error

Probability, expectation and standard deviation of Poisson distribution

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`