Probability, expectation and variance of exponential distribution

Error

There was an error loading the page.

Contributors

History

○

Xiaodan Leng 5 years, 8 months ago

Created this as a copy of Probability, expectation and variance of exponential distribution.

Name	Status	Author	Last Modified
Probability, expectation and variance of exponential distribution	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Probability, expectation and variance of exponential distribution	draft	Xiaodan Leng	10/07/2019 22:36

There are 4 other versions that do you not have access to.

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	1.250
ans2	number	1.563
ans3	number	0.743
period	string	minutes
ra	number	0.8
tol	number	0.001
tans3	number	0.743339223
thistime	number	1.7

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

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.

$P(X \lt \var{thistime}) = 1 -(e ^ {-\var{ ra} \times \var{thistime}}) = 1 -(e ^ { -\var{ra * thistime}}) = \var{ans3}$ 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
Gap-fill
Gap-fill		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 variance of exponential distribution

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `string`

Parts

Gap-fill

Loading...

Error

Probability, expectation and variance of exponential distribution

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`