Thread: Super Tough Probability Question

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Just do (a) directly with polar co-ordinates.
That's how you prove the normal density integrates to one.

Originally Posted by Porter1

Hi all, I have this question and I really need your help!

(a) Show that Г(1/2) = √(П) (<-Square root of Pi) by writing
Г(1/2) = ∫(0)->(∞) y^(-1/2) e^(-y) dy
by making the transformation y = (x^2)/2 and using the standard normal density.
[snip]

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.