Bivariate continuous distribution - marginals and conditional probability,

Error

There was an error loading the page.

Contributors

Newcastle University Mathematics and Statistics

History

○

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Created this.

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

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

Question statement

Suppose that a bivariate continuous random variable is defined on the region $R \subset \mathbb{R^2}$ given by:

$\var{a} \le x \le \var{a+b},\;\;\;\;\;\;\;\var{c} \le y \le \var{c+d}$ with joint PDF given by

$f(x,y)$ in

$R$ and zero otherwise.

In the following questions, you are asked to supply the limits of integration for the following computations:

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	4
c	integer	1
b	integer	4
d	integer	5
y1	integer	4
x1	integer	6

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..5)

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: `integer`

→ Used by:

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
4. Gap Gap 3. Number entry
  Add
Part b) 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
Part c) 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
Part d) 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

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

The probability $P(X \ge \var{x1})$ is given by:

$P(X\ge \var{x1})= \int_a^b \int_c^d f(x,y)dxdy$

Input the limits of integration here:

$a=\;$ ?Gap 0. $b=\;$ ?Gap 1.

$c=\;$ ?Gap 2. $d=\;$ ?Gap 3.

Advice

The probability $P(x \ge \var{x1})$ is given by:

$P(x \ge \var{x1})=\int_{\var{c}}^{\var{c+d}}\int_{\var{x1}}^{\var{a+b}} f(x,y) dx dy$

The marginal $f_X(x)$ of $X$ is:

$f_X(x)=\int_{\var{c}}^{\var{c+d}}f(x,y)dy$ and the range that

$f_X(x)$ is defined on is

$\var{a} \le x \le \var{a+b}$ .

The marginal $f_Y(y)$ of $Y$ is:

$f_Y(y)=\int_{\var{a}}^{\var{a+b}}f(x,y)dx$ and the range that

$f_Y(y)$ is defined on is

$\var{c} \le x \le \var{c+d}$ .

d) The conditional probability $P(Y \le \var{y1}|X \ge \var{x1})$ is calculated as follows:

$P(Y \le \var{y1}|X \ge \var{x1})=\frac{\int_{\var{c}}^{\var{y1}}\int_{\var{x1}}^{\var{a+b}} f(x,y) dx dy}{A}$

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
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
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
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

This question is used in the following exams:

Loading...

Error

Bivariate continuous distribution - marginals and conditional probability,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Bivariate continuous distribution - marginals and conditional probability,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`