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.
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 .