527ass3 - distributions you need to know the value o± a...

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642:527 ASSIGNMENT 3 FALL 2007 Multple-page homework must be STAPLED when handed in. Turn in starred problems Tuesday 09/25/2007. Section 4.5 8 9* Section 4.6 1 2* (see Remark 2 below) 6* 12 (a), (c)*, (d), (e)* 15 Remarks: 1. Problem 4.5.9 has two parts: you are frst asked to express Γ(1 / 2) in terms o± the Gaussian integral i 0 e - u 2 du , then to evaluate this integral. Gaussian integrals like this are important in various applications, and it is nice to know the standard trick (explained in the problem) ±or evaluating them. For example, the normal distribution o± a random variable is important in all statistical considerations, and to work with these
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Unformatted text preview: distributions you need to know the value o± a Gaussian integral. 2. In solving 4.6.2, don’t just plug into the given series ±or J ± 1 / 2 . Rather, start ±rom the beginning o± the Frobenius method. One point is that you will then see why there is no logarithm in the second solution! 3. At the bottom o± page 241 the book explains how to check your solutions to problem 12 using Maple, but i± you try this with 12(c) the answer given does not contain Bessel ±unctions? Why not? (This is not to be turned in—just to be thought about.) 1...
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