Question#1

The ‘probability of false alarm’ is given by…

(1)

… and setting is…

(2)

The problem is to find for which is . The method suggested in textbook is the bisection method, which is very inaccurate and requires long and tedious computation. Much better is the Newton-Raphson method, which solves an equation in the form via the iterative procedure…

(3)

In our case is…

(4)

In all cases the initial value is …

For in iterations we obtain the ‘stable value’ …

For in iterations we obtain the ‘stable value’ …

For in iterations we obtain the ‘stable value’ …

Kind regards