Exponential Distribution

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Brad's workspace :

Brad Allison

said

Ready to use

5 years, 7 months ago

History

○

Brad Allison 5 years, 7 months ago

Published this.

○

Brad Allison 5 years, 7 months ago

Gave some feedback: Ready to use

○

Brad Allison 5 years, 7 months ago

Created this.

There is only one version of this question that you have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

Lambda1	number	0.7
x1	integer	1
Ans1	number	0.3476097127
x2	integer	6
Ans2	number	0.0104969038
x3	integer	5
Ans3	number	0.0211381684
Lambda2	number	0.03
x4	integer	7
Ans4	number	0.810584246
x5	integer	6
j1	integer	5
Ans5	number	0.1392920236
x6	integer	6
j2	integer	5
Ans6	number	0.8607079764
x7	integer	9
Ans7	number	0.2591817793

			Name	Type	Generated Value

Lambda3	number	0.01
x8	integer	15
Ans8	number	0.8607079764
Ans9	number	0.7408182207

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

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: `number`

0.7

→ Used by:

Ans1
Ans2
Ans3

Advice
"Question 1" - prompt

Parts

Question 1 Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
7. Gap Gap 6. Number entry
  Add
Question 2 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.

(a) Given that $X\sim Exp(\var{Lambda1})$ . Find,

(i) $P(X=\var{x1})$

Answer:Gap 0.

(ii) $P(X=\var{x2})$

Answer:Gap 1.

(iii) $P(X=\var{x3})$

Answer:Gap 2.

(b) Given that $X\sim Exp(\var{Lambda2})$ . Find,

(i) $P(X>\var{x4})$

Answer:Gap 3.

(ii) $P(X<\var{x5})$

Answer:Gap 4.

(iii) $P(X\geq\var{x6})$

Answer:Gap 5.

(iv) $P(X\leq\var{x7})$

Answer:Gap 6.

Advice

Here are some tips on how to set out your work, as well as how to complete the questions. None of the answers given below have been rounded to what the question states.

Question 1

1a: $X\sim Exp(\var{Lambda1})$

(i) $P(X= x)=\lambda e^{-\lambda x} \rightarrow P(X= \var{x1})=\var{Lambda1}e^{-\var{lambda1} (\var{x1})} = \var{Ans1} $

(ii) $P(X= x)=\lambda e^{-\lambda x} \rightarrow P(X= \var{x2})=\var{Lambda1}e^{-\var{lambda1} (\var{x2})} = \var{Ans2} $

(ii) $P(X= x)=\lambda e^{-\lambda x} \rightarrow P(X= \var{x3})=\var{Lambda1}e^{-\var{lambda1} (\var{x3})} = \var{Ans3} $

1b: $X\sim Exp(\var{Lambda2})$

(i) $P(X\leq x)=1-e^{-\lambda x} \rightarrow P(X>\var{x4})=1-P(X\leq \var{x4}) =1-(1-e^{-\var{lambda2} (\var{x4})}) = \var{Ans4} $

(ii) $P(X\leq x)=1-e^{-\lambda x} \rightarrow P(X< \var{x5})=P(X\leq \var{x5}-1)=P(X\leq \var{j1})=1-e^{-\var{lambda2} (\var{j1})} = \var{Ans5} $

(iii) $P(X\leq x)=1-e^{-\lambda x} \rightarrow P(X\geq \var{x6})=1-P(X\leq \var{j2}) =1-(1-e^{-\var{lambda2} (\var{j2})}) = \var{Ans6} $

(iv) $P(X\leq x)=1-e^{-\lambda x} \rightarrow P(X\leq \var{x7}) =1-e^{-\var{lambda2} (\var{x7})} = \var{Ans7} $

Question 2

2a: $X\sim Exp(\var{Lambda3})$

(i) $P(X\leq x)=1-e^{-\lambda x} \rightarrow P(X>\var{x8})=1-P(X\leq \var{x8}) =1-(1-e^{-\var{lambda3} (\var{x8})}) = \var{Ans8} $

(ii) $P(X\leq x)=1-e^{-\lambda x} \rightarrow P(X_1>\var{x8}) \times P(X_2>\var{x8}) = (1-P(X_1\leq \var{x8}))\times (1-P(X_2\leq \var{x8})) = (1-(1-e^{-\var{lambda3} (\var{x8})})) \times (1-(1-e^{-\var{lambda3} (\var{x8})}))=\var{ans9} $

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
Number entry
Number entry		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 used in the following exams:

Week 3 test by Ellen Marshall in Ellen's workspace.
Test by Brad Allison in Brad's workspace.
Exponential Distribution by Brad Allison in Exam Version of Tests.
Ellen's copy of Exponential Distribution by Ellen Marshall in Ellen's workspace.
Ellen's copy of Exponential Distribution by Ellen Marshall in Exam Version of Tests.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Brad Allison 5 years, 7 months ago

Brad Allison 5 years, 7 months ago

Brad Allison 5 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

Loading...

Error

Exponential Distribution

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Brad Allison 5 years, 7 months ago

Brad Allison 5 years, 7 months ago

Brad Allison 5 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`