Subject: Reliability Engineering

1. A photo detector counts photons for 10 nano seconds to decide if a distant light source is emitting light. When the light source is not emitting light, some photons are still counted by the detector due to the ambient background radiation. The number of photons counted in 10 nanoseconds is modeled as a random variable X whose parameter has value ln (9) if the light source is not emitting light, and value in (27) if the source is emitting light. The maximum-likelihood detector decides that detection of light is the true if and only if the likelihood ratio = probability of detection when light is present (x)/probability of detection when light is not present (x) exceeds 1. (a) What value(s) of X result in a decision in favour of detecting of light? (b) Compute the false alarm probability PFA and the missed detection or false dismissal probability PMD of the maximum-likelihood decision rule.