A radar sends out 2000 pulses of a particular shape and listens for the return signal of each of these pulses. The radar receiver listens for bursts of pulses and declares a target if it detects k or more pulses in a short time interval. Through tests, the value of k is adjusted in the radar receiver until the probability of target declaration exeeds 0.95. Energy absorbing "paint" is then applied to the target. This material has the property that each millimeter of thickness reduces the radar receiver's probability of detecting a single pulse by 10%. How thick does the coating have to be to reduce our radar's probability of detection to 0.50 or smaller??
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