Segment 11. Random Deviates

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The direct YouTube link is http://youtu.be/4r1GlyisB8E

Links to the slides: PDF file or PowerPoint file

Problems

To Calculate

1. For the Cauchy distribution (Segment 8, Slide 3), find the inverse function of the CDF.

2. In your favorite programming language, write a function that returns independent Cauchy deviates.

To Think About

1. Suppose you want a function that returns deviates for StudentFailed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (\nu)} . Could you use the Cauchy pdf (or some scaling of it) as a bounding function in a rejection method? How efficient is this (i.e., what fraction of the time does it reject)?

2. Explain the three inequality tests in the "while" statement in Leva's algorithm (slide 7) and why they are hooked together with logical operators in the way shown.

Class Activity

Build your own random number generator