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On the off chance you just need the Student t distribution:

See this Sage documentation and search for t-distribution.

sage: nu = 1
sage: T = RealDistribution('t', nu)
sage: T.get_random_element() # random
sage: T.distribution_function(0)
sage: T.cum_distribution_function(1)
sage: T.cum_distribution_function_inv(.5)

The word "student's" was removed in the change associated with Trac 9080 which added F-distribution. It will be a lot more work to have the distributions well integrated with the rest of Sage, but we could put that word back in - I suppose it was my fault, since I reviewed the ticket.

Also, see this sagenb worksheet for someone plotting the actual pdf.