Signal-to-Noise Ratio: If random variable X has mean μ ¹ 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

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Signal-to-Noise Ratio: If random variable X has mean μ ¹ 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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