Consider nine 1 cm _1 cm PMTs arranged in 3 _3 array (Figure P8.2). The output of each PMT to a…

Consider nine 1 cm _1 cm PMTs arranged in 3 _3 array
(Figure P8.2). The output of each PMT to a scintillation event is modeled as

where (x, y) is the location of the scintillation event, and
(xi, yi) is the center of the i-th PMT.

Figure P8.2 See Problem 8.8.

(a) Find the output of each PMT for a scintillation event
that occurs at (_0.5, 0.5) cm.

(b) What is the estimated position of the scintillation
event?

(c) Is

Consider nine 1 cm _1 cm PMTs arranged in 3 _3 array
(Figure P8.2). The output of each PMT to a scintillation event is modeled as

where (x, y) is the location of the scintillation event, and
(xi, yi) is the center of the i-th PMT.

Figure P8.2 See Problem 8.8.

(a) Find the output of each PMT for a scintillation event
that occurs at (_0.5, 0.5) cm.

(b) What is the estimated position of the scintillation
event?

(c) Is the estimated position the same as its true position?
If not, explain why

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