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I am not familiar with the change-of-variable technique that the question refers to. Does anyone have an idea what is meant and how one should go about doing it?

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  • Note: this is not a homework question, but I'm studying for exams. – rbm Oct 21 '13 at 09:12
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    Most likely by `the change-of-variables technique` is meant the usual method involving Jacobians. However, the result that you are asked to prove is false unless the univariate standard normal random variables are **independent** random variables. See [this answer](http://stats.stackexchange.com/a/30205/6633) for a great description of how two normal random variables can fail to have a bivariate normal distribution. – Dilip Sarwate Oct 21 '13 at 12:16
  • @DilipSarwate Thank you. I assume though that that is probably what the professor meant. Could you show me how the method with the Jacobians works assuming that that is so? – rbm Oct 21 '13 at 12:30
  • See [this document](http://courses.engr.illinois.edu/ece313/fa2000/ppt/Lecture39.pdf) for how the Jacobian method applies to the special case of linear transformations of normal random variables. – Dilip Sarwate Oct 21 '13 at 13:01
  • @DilipSarwate Hmmh, I still don't really understand how it would work in this case. Could you please show me? – rbm Oct 21 '13 at 17:02

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