Signal-to-Noise Ratio: If random variable X has mean μ not equal to 0 and standard deviation s > 0, the ratio r = |μ| /s is called the measurement signal-to-noise ratio (SNR) of X (sometimes SNR is defined as the square of this quantity.) The idea is that X can be expressed as X = μ+ (X − μ), with μ representing a deterministic constant-valued “signal”, and (X − μ) the random zero-mean “noise.” In applications, it is desirable to have an upper-bound, with a probabilistic guarantee, on the magnitude of the relative deviation of X from its mean μ, defined as D = |(X − μ) /μ| . That is, we are interested in finding a positive number a, such that P(D ≤ a) ≥ c where c is a pre-specified numbe
Signal-to-Noise Ratio: If random variable X has mean μ not equal to 0 and standard deviation s > 0, the ratio r = |μ| /s is called the measurement signal-to-noise ratio (SNR) of X (sometimes SNR is defined as the square of this quantity.) The idea is that X can be expressed as X = μ+ (X − μ), with μ representing a deterministic constant-valued “signal”, and (X − μ) the random zero-mean “noise.” In applications, it is desirable to have an upper-bound, with a probabilistic guarantee, on the magnitude of the relative deviation of X from its mean μ, defined as D = |(X − μ) /μ| . That is, we are interested in finding a positive number a, such that P(D ≤ a) ≥ c where c is a pre-specified number representing our confidence in the upper-bound. If r = 10, provide an upper-bound a, with confidence level c = 0.95.
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