# Segment 11. Random Deviates

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### 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 Student<math>(\nu)</math>. 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.