exercise:5541528963: Difference between revisions
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The joint density function of the ''logarithm'' of the two random variables <math>X</math> and <math>Y</math> equals <math>f(x,y)</math>. Which of the following expressions represent the joint density function of <math>X</math> and <math>Y</math>? | The joint density function of the ''logarithm'' of the two random variables <math>X</math> and <math>Y</math> equals <math>f(x,y)</math>. Which of the following expressions represent the joint density function of <math>X</math> and <math>Y</math>? | ||
< | <ul class="mw-excansopts"> | ||
<li><math>y^{-1}x^{-1}f(\ln(x),\ln(y))</math></li> | <li><math>y^{-1}x^{-1}f(\ln(x),\ln(y))</math></li> | ||
<li><math>f(\ln(x),\ln(y))</math></li> | <li><math>f(\ln(x),\ln(y))</math></li> | ||
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<li><math>e^x e^yf(e^x,e^y)</math></li> | <li><math>e^x e^yf(e^x,e^y)</math></li> | ||
<li><math>x^{-1}f(\ln(x),x) + y^{-1}f(x,\ln(y))</math></li> | <li><math>x^{-1}f(\ln(x),x) + y^{-1}f(x,\ln(y))</math></li> | ||
</ | </ul> | ||
Revision as of 21:11, 17 March 2024
The joint density function of the logarithm of the two random variables [math]X[/math] and [math]Y[/math] equals [math]f(x,y)[/math]. Which of the following expressions represent the joint density function of [math]X[/math] and [math]Y[/math]?
- [math]y^{-1}x^{-1}f(\ln(x),\ln(y))[/math]
- [math]f(\ln(x),\ln(y))[/math]
- [math]y^{-1}x^{-1}f(x,y)[/math]
- [math]e^x e^yf(e^x,e^y)[/math]
- [math]x^{-1}f(\ln(x),x) + y^{-1}f(x,\ln(y))[/math]