Examples of equal time rule in the following topics:
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- The multiplication rule states that the probability that $A$ and $B$ both occur is equal to the probability that $B$ occurs times the conditional probability that $A$ occurs given that $B$ occurs.
- In probability theory, the Multiplication Rule states that the probability that $A$ and $B$ occur is equal to the probability that $A$ occurs times the conditional probability that $B$ occurs, given that we know $A$ has already occurred.
- This rule can be written:
- Switching the role of $A$ and $B$, we can also write the rule as:
- The rule is useful when we know both $P(B)$ and $P(A|B)$, or both $P(A)$ and $P(B|A).$
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- The rule simply states:
- More specifically, given events $A_1$, $A_2$ and $B$, Bayes' rule states that the conditional odds of $A_1:A_2$ given $B$ are equal to the marginal odds $A_1:A_2$ multiplied by the Bayes factor or likelihood ratio.
- Rationally, Bayes' rule makes a great deal of sense.
- Furthermore, Bayes' rule can be applied iteratively.
- This allows for Bayesian principles to be applied to various kinds of evidence, whether viewed all at once or over time.
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- Kirchhoff's junction rule states that at any circuit junction, the sum of the currents flowing into and out of that junction are equal.
- Kirchhoff's junction rule, also known as Kirchhoff's current law (KCL), Kirchoff's first law, Kirchhoff's point rule, and Kirchhoff's nodal rule, is an application of the principle of conservation of electric charge.
- Kirchhoff's junction rule states that at any junction (node) in an electrical circuit, the sum of the currents flowing into that junction is equal to the sum of the currents flowing out of that junction.
- This law is founded on the conservation of charge (measured in coulombs), which is the product of current (amperes) and time (seconds).
- We justify Kirchhoff's Rules from diarrhea and conservation of energy.
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- The derivative of the exponential function is equal to the value of the function.
- The rate of increase of the function at $x$ is equal to the value of the function at $x$.
- If a variable's growth or decay rate is proportional to its size—as is the case in unlimited population growth, continuously compounded interest, or radioactive decay—then the variable can be written as a constant times an exponential function of time.
- Furthermore, for any differentiable function $f(x)$, we find, by the chain rule:
- Since the slope of the red tangent line (the derivative) at $P$ is equal to the ratio of the triangle's height to the triangle's base (rise over run), and the derivative is equal to the value of the function, $h$ must be equal to the ratio of $h$ to $b$.
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- Kirchhoff's loop rule states that the sum of the emf values in any closed loop is equal to the sum of the potential drops in that loop.
- Kirchhoff's loop rule (otherwise known as Kirchhoff's voltage law (KVL), Kirchhoff's mesh rule, Kirchhoff's second law, or Kirchhoff's second rule) is a rule pertaining to circuits, and is based on the principle of conservation of energy.
- Given that voltage is a measurement of energy per unit charge, Kirchhoff's loop rule is based on the law of conservation of energy, which states: the total energy gained per unit charge must equal the amount of energy lost per unit of charge.
- Rearranged, this is emf=Ir+IR1+IR2, meaning that the emf equals the sum of the IR (voltage) drops in the loop.
- Kirchhoff's loop rule states that the sum of all the voltages around the loop is equal to zero: v1 + v2 + v3 - v4 = 0.
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- Democracy requires that all citizens have an equal opportunity to express their opinion.
- Theoretically, Aristotle contrasted rule by the many (democracy/polity) with rule by the few (oligarchy/aristocracy) and with rule by a single person (tyranny or autocracy/monarchy).
- There are two main aspects of freedom: (1) being ruled and ruling in turn, since everyone is equal according to number, not merit, and; (2) to be able to live as one pleases.
- Under minimalism, democracy is a system of government in which citizens give teams of political leaders the right to rule in periodic elections.
- According to this minimalist conception, citizens cannot and should not rule because, for example, on most issues, most of the time, they have no clear views or their views are not well-founded.
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- For example, consider the experiment of flipping a coin two times.
- It is always greater than or equal to zero, and less than or equal to one.
- An event with a probability of $0.5$ will occur half of the time.
- The sum of the probabilities of all possibilities must equal $1$.
- The probability that no heads occurs is $1/4$, which is equal to $1-3/4$.
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- Aristocracy refers to the rule by elite citizens; a system of governance in which a person who rules in an aristocracy is an aristocrat.
- It has come to mean rule by "the aristocracy" who are people of noble birth.
- The Roman Republic made Dictators to lead during times of war.
- In modern times, an Autocrat's rule is not stopped by any rules of law, constitutions, or other social and political institutions.
- These people may spread power equally or not equally.
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- If behavior is constrained or influenced by rules, rules of thumb or habits, the nature of those rules and the process by which the rules evolves is of interest to economists.
- Rules may by implicit or explicit.
- If over time a particular problem is always, or nearly always, resolved by a specific approach, that approach becomes a habit or rule of thumb.
- If a habit, institution or custom fails to provide reasonable solutions over a period of time, new solutions emerge to become new rules, customs or institutions.
- Other incentives may be equally as important.
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- From the end of the Middle Ages to modern times, composers and performers in western Europe gradually developed widely accepted standards for tuning, melody, harmony, meter, notation, form, counterpoint and other music basics.
- These rules are a sort of grammar for the language of music.
- But they all use the same musical "language" and follow basically the same rules.
- What are the rules of this European musical language?
- The short answer is: Western music is generally tonal, based on major or minor scales, using an equal temperament tuning, in an easy-to-recognize meter, with straightforward rhythms, fairly strict rules on harmony and counterpoint, and not much improvisation.