BS3.6

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Bill Foster

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Bill Foster 12 years, 2 months ago

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Question statement

The time, in {period} between {this} follows an exponential distribution with rate $\var{ra}$ i.e.

$X \sim \operatorname{exp}(\var{ra})$

Give any introductory information the student needs.

			Name	Type	Generated Value

that	string	two customers arriving
this	string	customer arrivals at the RyanJ
ans1	number	2.500
ans2	number	6.250
ans3	number	0.356
period	string	minutes
ra	number	0.4
tol	number	0.001
tans3	number	0.3559635789
thistime	number	1.1

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
"two customers arriving "

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`

two customers arriving

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
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.

Find $\operatorname{E}[X]$ between {this}:

$\operatorname{E}[X]=$ Gap 0.{period} (enter as a decimal correct to 3 decimal places).

Find $\operatorname{Var}(X)$ :

$\operatorname{Var}(X)=$ Gap 1. (enter as a decimal correct to 3 decimal places).

Advice

If $X \sim \operatorname{exp}(\lambda)$ then $\displaystyle \operatorname{E}[X] =\frac{1}{\lambda}$ and $\displaystyle \operatorname{Var}(X)=\frac{1}{\lambda^2}$ .

Also $P(X \lt a)=1-e^{-\lambda a}$ .

a)

If $X \sim \operatorname{exp}(\var{ra})$ then:

$\displaystyle \operatorname{E}[X] =\frac{1}{\lambda}=\frac{1}{\var{ra}}=\var{ans1}$ to 3 decimal places.

$\displaystyle \operatorname{Var}(X) =\frac{1}{\lambda^2}=\frac{1}{\var{ra}^2}=\var{ans2}$ to 3 decimal places.

b)

$P(X \lt \var{thistime}) = 1 -(e ^ {-\var{ ra} \times \var{thistime}}) = 1 -(e ^ { -\var{ra * thistime}}) = \var{ans3}$ to 3 decimal places.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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History

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Checkpoint description

Bill Foster 12 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `string`

Parts

Gap-fill

a)

b)

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BS3.6

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 12 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

a)

b)

Generated value: `string`