Heres the question:

In certain signal detection problems (eg, radar or sonar) the probability of false alarm (FA) (ie of saying that a certain signal is present in the data when it actually is not) is given by:

.........∞

pFA = ∫ _______

__1_________x^p/2-1 e-x/2 dx

.........η

**...Γ(p/2) 2^p/2**

Where

**η**is called the detection threshold. If p is an even number, it can be shown that reduces to the finite series:

..........................(p/2)-1

pFA = e^(-1/2

**η**) ...

**Σ ......**_

__1___..(

___) ^k__

**_η**...........................k=0 .......k! .... 2

P.S

. are used to align the values correctly

The detection threshold

**η**is a very important design parameter in signal detectors. Often it is desired to specify an acceptable value for pFA (where 0 < pFA <1), and then it is necessary to solve nonlinear equation for

**η.**Let p = 6. Use the bisection method to find

**η**for:

a) pFA = 0.001

b) pFA = 0.01

c) pFA = 0.1

Instructions on how problem was solved will be appreciated as well so I can undertand what was done