We can show that the normal density function integrates to unity by showing that, if u >
Chapter 4, Problem 4.194(choose chapter or problem)
We can show that the normal density function integrates to unity by showing that, if u > 0, 1 2 " e(1/2)uy2 dy = 1 u . This, in turn, can be shown by considering the product of two such integrals: 1 2 " e(1/2)uy2 dy " e(1/2)ux2 dx = 1 2 " " e(1/2)u(x2+y2) dx dy. By transforming to polar coordinates, show that the preceding double integral is equal to 1/u. *4
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