Devise simpler bounds v∗ +, v∗ − (or use the maximum) and derive a non-setup version for Algorithm C3. Compare its performance. Show that the distribution function for the Student’s t distribution...

Devise simpler bounds v∗ +, v∗ − (or use the maximum) and derive a non-setup version for Algorithm C3. Compare its performance.

Show that the distribution function for the Student’s t distribution with three degrees of freedom is

                        F(x) = 1 π √ 3  x 2(1 + x2/3) + √ 3 tan−1