Consider an optical communication system that transmits a symbol "1" by turning a laser onfor 200 nanoseconds, and a "0" by turn
ing the laser off for 200 nanoseconds. A photon count-ing device counts the number of photons in the 200 nanosecond time interval (synchronizedwith the transmitting laser). Assume that the number of photons measured within a giveninterval (200 nanoseconds) is a Poisson random variable with parametersλ1= 5 andλ0= 1,depending on whether the laser is on or off. Note that even when the laser is off, it still emitsa random number of photons due to the dark current. Also assume "0" is 5 times as likely as"1" to be transmitted. Suppose that the photon counting device detects 5 photons in a giventime interval. What is the probability that a "0" was sent?Hint: This problem requires the use of conditional PMF and Bayes’ rule.
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The local minima of are (x, f(x)) = (-1.5, 0) and (7.980, 609.174)
The function is given as:
See attachment for the graph of the function f(x)
From the attached graph, we have the following minima:
Minimum = (-1.5, 0)
Minimum = (7.980, 609.174)
The above means that, the local minima are
(x, f(x)) = (-1.5, 0) and (7.980, 609.174)
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