The integral

arises in probability theory.

(a) Consult the library or Internet to find how this integral relates to the calculationof a probability using the Normal distribution. Provide a summary of what you find and identify what probability the integral calculates (around 1-2 pages).

(b) Give a reasonable argument to show that

 (c) The above double integral can not be evaluated using standard integration techniques.

Instead we must first transform the integral to polar coordinates.

i. Consult the library or Internet to find out the way in which transforming to polar coordinates works for double integrals formulated in Cartesian coordinates.

ii. Evaluate I₂ by transforming the double integral in Equation (1) to polar coordinates.

(d) Use your result from Part (c)(ii) to show that I =√π/2