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Mathematics 340 - Fall 2013

Homework

Chapter 6

Problems: 6.11, 6.21, 6.23, 6.27, 6.28

Theoretical Exercises: 6.4, 6,7

Note: For 6.4, assume $D = 1$. Also, the answer in the text uses different parameters. Using the parameters from class, the answer is $\frac{2L}{\pi}(1 - \cos(\alpha)) + \frac{1}{\pi}(\pi - 2\alpha)$, where $\alpha = \sin^{-1}\left(\frac{1}{L}\right)$.

Also: Suppose $X$ and $Y$ are independent random variables, each uniformly distributed on $(0, 1)$. Find the probability density function of $Z = \frac{Y}{X}$.

For problem set due 18 November: Suppose $X$ and $Y$ are independent random variables, each uniformly distributed on $(0, 1)$. Find the probability density function of $Z = XY$.