given the following Probability density function:(adsbygoogle = window.adsbygoogle || []).push({});

f x,y(x,y) = { 0.5, ( 0<y<1, 2y-x<2, 2y+x<2 }

0, else

and i need to find f z(z) while z=y-x

i got really confused while trying to calculate the borders of x and y for the integration.

i would be really thankful for someone explaining me how to come to the borders slow and step by step.

i got to the following equations: y < 2-z , y < (2+z)/3 , x < 2-z, x < (2-2z)/3

but i don't know how to resume from here. it said on the solution that borders are 0 to (2-2z)/3 for y and y-z to 2-2y for x. why?

thanks in advance for any help

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Transformation of two dimensional random var

Loading...

Similar Threads for Transformation dimensional random | Date |
---|---|

I Understanding the transformation of skewness formula | Apr 4, 2018 |

B Viability of log-log transformation for some data | May 18, 2017 |

A Covariance matrix for transformed variables | Sep 30, 2016 |

I Change of variables many-to-many transformation | Sep 6, 2016 |

N-dimensional Universal Turing Machine? | Dec 26, 2011 |

**Physics Forums - The Fusion of Science and Community**