A sensor produces measurements where is the constant quantity being measured, represents short-term zero-mean random noise, and is a slowly varying calibration offset that is not assumed to average to zero. An engineer assumes that the may be treated as IID and therefore argues that the Law of Large Numbers (LLN) guarantees converges in probability to as . Which assessment is correct?

Question

A sensor produces measurements    where    is the constant quantity being measured,    represents short-term zero-mean random noise, and    is a slowly varying calibration offset that is not assumed to average to zero. An engineer assumes that the    may be treated as IID and therefore argues that the Law of Large Numbers (LLN) guarantees    converges in probability to    as   . Which assessment is correct?

Accepted Answer

The argument is incorrect because the drift can make the    non-identically distributed, and there is no guarantee that the average drift tends to zero.

Answer

The argument is correct because averaging removes any disturbance as the number of measurements increases.

Answer

The argument is correct because the Central Limit Theorem guarantees that the sample mean converges to   , even when calibration drift is present.

Answer

The argument is correct provided more than 30 measurements are collected, since the sample mean can then be treated as approximately equal to   .

Answer

The argument is incorrect because the LLN cannot be applied to continuous-valued sensor measurements.

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A sensor produces measurements where is the constant quantity being measur...

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