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In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let () = (), where both f and g are differentiable and ()
Statistical proof is the rational demonstration of degree of certainty for a proposition, hypothesis or theory that is used to convince others subsequent to a statistical test of the supporting evidence and the types of inferences that can be drawn from the test scores.
This is called the addition law of probability, or the sum rule. That is, the probability that an event in A or B will happen is the sum of the probability of an event in A and the probability of an event in B, minus the probability of an event that is in both A and B. The proof of this is as follows: Firstly,
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
The expression "statistical proof" may be used technically or colloquially in areas of pure mathematics, such as involving cryptography, chaotic series, and probabilistic number theory or analytic number theory. [23] [24] [25] It is less commonly used to refer to a mathematical proof in the branch of mathematics known as mathematical statistics.
In statistics, the delta method is a method of deriving the asymptotic distribution of a random variable. It is applicable when the random variable being considered can be defined as a differentiable function of a random variable which is asymptotically Gaussian .
In combinatorics, the rule of division is a counting principle. It states that there are n/d ways to do a task if it can be done using a procedure that can be carried out in n ways, and for each way w, exactly d of the n ways correspond to the way w. In a nutshell, the division rule is a common way to ignore "unimportant" differences when ...
Among the applications of the product rule is a proof that = when n is a positive integer (this rule is true even if n is not positive or is not an integer, but the proof of that must rely on other methods). The proof is by mathematical induction on the exponent n.