The Standard Cauchy Distribution
The ti distribution is also known as the standard Cauchy distribution. Its density is






where the second equality follows from (4.36), and its characteristic function is
Vh(t) = exp(t ).
The latter follows from the inversion formula for characteristic functions:







See Appendix 4.A. Moreover, it is easy to verify from (4.39) that the expectation of the Cauchy distribution does not exist and that the second moment is infinite.
4.6.2. The F Distribution
Let Xm ~ x2 and Yn ~ x2, where Xm and Yn are independent. Then the distribution of the random variable
F _ Xm / m Yn/n
is said...
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