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Multi tool use

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Setting the limits when integrating a bivariate density function

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$begingroup$

This specific question is asking to find the values of $k$ such that the function is a density function.

$$f(x,y)=begincasesk(1-y) &text if 0<x<y<1, \ 0 &text otherwise. endcases$$

Essentially, I know the essence of the problem will be integrating and then equating to $1$ etc., what I am having trouble with is however setting the limits of the double integral. I understand that with respect to y, the limits would be between $1$ and $x$, however it confuses me that $x_1$ is set between $1$ and $0$, rather than $y$ and $0$.

Thanks!

probability

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edited yesterday

Max

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asked yesterday

Mark ZakhemMark Zakhem

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Mark Zakhem is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
  $endgroup$
  – José Carlos Santos
  yesterday
  

  
  
  
  

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0

$begingroup$

This specific question is asking to find the values of $k$ such that the function is a density function.

$$f(x,y)=begincasesk(1-y) &text if 0<x<y<1, \ 0 &text otherwise. endcases$$

Essentially, I know the essence of the problem will be integrating and then equating to $1$ etc., what I am having trouble with is however setting the limits of the double integral. I understand that with respect to y, the limits would be between $1$ and $x$, however it confuses me that $x_1$ is set between $1$ and $0$, rather than $y$ and $0$.

Thanks!

probability

share|cite|improve this question

edited yesterday

Max

564317

asked yesterday

Mark ZakhemMark Zakhem

1

New contributor

Mark Zakhem is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
  $endgroup$
  – José Carlos Santos
  yesterday
  

  
  
  
  

add a comment | 

$begingroup$

This specific question is asking to find the values of $k$ such that the function is a density function.

$$f(x,y)=begincasesk(1-y) &text if 0<x<y<1, \ 0 &text otherwise. endcases$$

Essentially, I know the essence of the problem will be integrating and then equating to $1$ etc., what I am having trouble with is however setting the limits of the double integral. I understand that with respect to y, the limits would be between $1$ and $x$, however it confuses me that $x_1$ is set between $1$ and $0$, rather than $y$ and $0$.

Thanks!

probability

share|cite|improve this question

edited yesterday

Max

564317

asked yesterday

Mark ZakhemMark Zakhem

1

New contributor

Mark Zakhem is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited yesterday

Max

564317

asked yesterday

Mark ZakhemMark Zakhem

1

New contributor

Mark Zakhem is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited yesterday

Max

564317

asked yesterday

Mark ZakhemMark Zakhem

1

New contributor

Mark Zakhem is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited yesterday

Max

564317

edited yesterday

Max

564317

asked yesterday

Mark ZakhemMark Zakhem

1

New contributor

Mark Zakhem is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked yesterday

Mark ZakhemMark Zakhem

1