2 8. The function P(:1:) = e1 is fundamental in probability. (a) Sketch the graph of P(:z:). Explain why it is called a. \"bell curve.\" (b) Compute I = f 332 dz using the following brilliant strategy of Gauss: 00 i. Instead of computing I , compute 12 = (f 6*\"2 dm) (f e'yz dy). 00 -W ii. Rewrite I 2 as an integral of the form f] f (:12,y) (M where R is the entire Cartesian plane. R iii. Convert that integral to polar coordinates. iv. Evaluate to nd I 2. Deduce the value of I. Amazingly, it can be mathematically proven that there is NO elementary function 62(3) (that is, function built up from 511135, cosines, exponentials, and roots using "usual\" operations) for which Q' (3;) = P($)_