Solved: Normal distribution An important integral in
Chapter 13, Problem 71(choose chapter or problem)
Normal distribution An important integral in statistics associated with the normal distribution is I = 1 _ -_ e-x2 dx. It is evaluated in the following steps. a. Assume that I 2 = a L _ -_ e-x2 dxb a L _ -_ e-y2 dyb = L _ -_ L _ -_ e-x2 -y2 dxdy, where we have chosen the variables of integration to be x and y and then written the product as an iterated integral. Evaluate this integral in polar coordinates and show that I = 1p. Why is the solution I = -1p rejected? T b. Evaluate 1 _ 0 e-x2 dx, 1 _ 0 xe-x2 dx, and 1 _ 0 x2 e-x2 dx (using part (a) if needed).
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