Let x be the number of photons counted by a receiver in an optical communication system. it is known that x is a poisson random variable with rate λ1 when a signal is present and a poisson random variable with rate λ0 < λ1 when a signal is absent. the probability that the signal is present is p. suppose that we observe x = k photons. we want to determine a threshold t such that if k ≥ t then we claim that the signal is present; and if k < t then we claim that the signal is absent. what is this t?

207/8 is the right

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step-by-step explanatio89

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

i believe it is 0.1m because the measurement of 30.4m limits how precise you can be

you can only be as precise as the least precise measurement