Question

A detector counts pulse for every 100 picoseconds to decide if a distant source is emitting wave. When the wave source is not emitting wave of specific wavelength, some wave (of specific wavelength) are still counted by the detector due to the ambient background noise. The number of wave counted in 10 microseconds is modeled as a random variable X whose parameter λ has a value of ln(7) if the wave source is not emitting wave, and a value of ln(32) if the source is emitting wave. The maximum-likelihood detector decides that detection of light is true if and only if the likelihood ratio, calculated as (probability of detection when wave is present(X))/ (Probability of detection when wave is not present(X)) , exceeds 1.

Answer the following questions:

a. What value(s) of X result in a decision in favour of detecting of wave?

b. Compute the false alarm probability (detection when wave is not present) and the missed detection of the maximum-likelihood decision rule.

Answer 1