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0 (error-free) 001 0 010 0 100 0 111 1 (error-free) 110 1 101 1 011 1 ... Cyclic redundancy checks (CRCs) can correct 1-bit errors for messages at most ...
A checksum of a message is a modular arithmetic sum of message code words of a fixed word length (e.g., byte values). The sum may be negated by means of a ones'-complement operation prior to transmission to detect unintentional all-zero messages.
For a value that is sampled with an unbiased normally distributed error, the above depicts the proportion of samples that would fall between 0, 1, 2, and 3 standard deviations above and below the actual value.
This is especially true of cryptographic hash functions, which may be used to detect many data corruption errors and verify overall data integrity; if the computed checksum for the current data input matches the stored value of a previously computed checksum, there is a very high probability the data has not been accidentally altered or corrupted.
Note that the steeper green and red regression estimates are more consistent with smaller errors in the y-axis variable. Regression dilution, also known as regression attenuation, is the biasing of the linear regression slope towards zero (the underestimation of its absolute value), caused by errors in the independent variable.
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By selecting the witness as a random string, the verifier is a probabilistic polynomial-time Turing Machine whose probability of accepting x when x is in X is large (greater than 1/2, say), but zero if x ∉ X (for RP); of rejecting x when x is not in X is large but zero if x ∈ X (for co-RP); and of correctly accepting or rejecting x as a ...
Despite the fact that the likelihood ratio in favor of the alternative hypothesis over the null is close to 100, if the hypothesis was implausible, with a prior probability of a real effect being 0.1, even the observation of p = 0.001 would have a false positive rate of 8 percent. It wouldn't even reach the 5 percent level.