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The critical value corresponds to the cumulative distribution function of the F distribution with x equal to the desired confidence level, and degrees of freedom d 1 = (n − p) and d 2 = (N − n). The assumptions of normal distribution of errors and independence can be shown to entail that this lack-of-fit test is the likelihood-ratio test of ...
Formulas in the B column multiply values from the A column using relative references, and the formula in B4 uses the SUM() function to find the sum of values in the B1:B3 range. A formula identifies the calculation needed to place the result in the cell it is contained within. A cell containing a formula, therefore, has two display components ...
From its first version Excel supported end-user programming of macros (automation of repetitive tasks) and user-defined functions (extension of Excel's built-in function library). In early versions of Excel, these programs were written in a macro language whose statements had formula syntax and resided in the cells of special-purpose macro ...
For example, the formula "a AND NOT b" is satisfiable because one can find the values a = TRUE and b = FALSE, which make (a AND NOT b) = TRUE. In contrast, " a AND NOT a " is unsatisfiable. SAT is the first problem that was proven to be NP-complete —this is the Cook–Levin theorem .
Subtracting nearby numbers in floating-point arithmetic does not always cause catastrophic cancellation, or even any error—by the Sterbenz lemma, if the numbers are close enough the floating-point difference is exact.
It is assumed that the value of a function f defined on [,] is known at + equally spaced points: < < <.There are two classes of Newton–Cotes quadrature: they are called "closed" when = and =, i.e. they use the function values at the interval endpoints, and "open" when > and <, i.e. they do not use the function values at the endpoints.
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.