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- Nov 25th 2009, 08:25 PMPorter1Super Tough Probability Question
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- Nov 26th 2009, 12:42 AMmatheagle
Just do (a) directly with polar co-ordinates.

That's how you prove the normal density integrates to one. - Nov 26th 2009, 08:00 AMawkward
You can work this out from basics as suggested by MathEagle, but if you are allowed to assume some basic knowledge of the Normal distribution there is a shortcut, which I think is probably what you are intended to do--

After you make the substitution, you should have

which is equal to

Based on your knowledge of the Normal distribution, you should know the value of .

Take it from there.