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Normality can be used for acid-base titrations. For example, sulfuric acid (H 2 SO 4) is a diprotic acid. Since only 0.5 mol of H 2 SO 4 are needed to neutralize 1 mol of OH −, the equivalence factor is: f eq (H 2 SO 4) = 0.5. If the concentration of a sulfuric acid solution is c(H 2 SO 4) = 1 mol/L, then its normality is 2 N. It can also be ...
Bayes' theorem says that the posterior probability measure is proportional to the product of the prior probability measure and the likelihood function. Proportional to implies that one must multiply or divide by a normalizing constant to assign measure 1 to the whole space, i.e., to get a probability measure.
At 15.6 °C (60.1 °F), the density of a saturated solution is 0.88 g/ml; it contains 35.6% ammonia by mass, 308 grams of ammonia per litre of solution, and has a molarity of approximately 18 mol/L. At higher temperatures, the molarity of the saturated solution decreases and the density increases. [8]
A different technique, which goes back to Laplace (1812), [3] is the following. Let = =. Since the limits on s as y → ±∞ depend on the sign of x, it simplifies the calculation to use the fact that e −x 2 is an even function, and, therefore, the integral over all real numbers is just twice the integral from zero to infinity.
In analytical chemistry, a solution of any substance which contains one equivalent per litre is known as a normal solution (abbreviated N), so the example sodium hydroxide solution would be 0.0893 N. [3] [13] The relative uncertainty (u r) in the measured concentration can be estimated by assuming a Gaussian distribution of the measurement ...
Asymptotic normality, in mathematics and statistics; Complete normality or normal space, Log-normality, in probability theory; Normality (category theory) Normality (statistics) or normal distribution, in probability theory; Normality tests, used to determine if a data set is well-modeled by a normal distribution
The annotation, d a°C/b°C, indicates density of solution at temperature a divided by density of pure water at temperature b known as specific gravity. When temperature b is 4 °C, density of water is 0.999972 g/mL.
In measure-theoretic probability theory, the density function is defined as the Radon–Nikodym derivative of the probability distribution relative to a common dominating measure. [5] The likelihood function is this density interpreted as a function of the parameter, rather than the random variable. [6]