Consider the following experiment. We have a radioactive sample situated at unit distance from a line of sensors. Each time a sensor detects a particle emitted from the

sample we obtain a reading of the position of the sensor in the x axis (we assume that we have so many sensors that you can model this position as a continuous random variable). We model the measurements as an i.i.d. sequence distributed as a random variable M = c+X where the pdf of X is symmetric around the origin, that is ?fX?(x)=fX?(?x)? for all real numbers x. Your task is to estimate the position of the sample c from these data.

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