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Page "Probability interpretations" ¶ 13
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If and random
If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.
If it were wholly random and unrelated, it would be 2.0, assuming the five classes were equal in n, which approximately they are.
If no address is provided, one is picked at random from the " base subnet ", 0.
If are independent and identically distributed random variables, each with a standard Cauchy distribution, then the sample mean has the same standard Cauchy distribution ( the sample median, which is not affected by extreme values, can be used as a measure of central tendency ).
If one watches a bacterium swimming in a uniform environment, its movement will look like a random walk with relatively straight swims interrupted by random tumbles that reorient the bacterium.
If it is moving in the wrong direction, it will tumble sooner and try a new direction at random.
If the affected bits are independently chosen at random, the probability of a two-bit error being undetected is 1 / n.
If we insert vertices in random order, it turns out ( by a somewhat intricate proof ) that each insertion will flip, on average, only O ( 1 ) triangles – although sometimes it will flip many more.
If a game has a board, the board is usually irregular rather than uniform or symmetric ( like Risk rather than chess or Scrabble ); the board is often random ( like Settlers of Catan ) or has random elements ( like Tikal ).
If X is a positive random variable and q > 0 then for all ε > 0
If μ is an unknown constant and W is random noise with probability density, then has probability density and is therefore a location family ..
If the degree of underrepresentation is small, the sample can be treated as a reasonable approximation to a random sample.
If the key is truly random, as large as or greater than the plaintext, never reused in whole or part, and kept secret, the ciphertext will be impossible to decrypt or break without knowing the key.
If an individual coin toss or the roll of dice is considered to be a random event, then if repeated many times the sequence of random events will exhibit certain patterns, which can be studied and predicted.
If the random variable is real-valued ( or more generally, if a total order is defined for its possible values ), the cumulative distribution function gives the probability that the random variable is no larger than a given value ; in the real-valued case it is the integral of the density.
If indeed an answer comes, the time and place it comes is considered random.
If X is a real-valued random variable and a is a number then the event X ≤ a is the set of outcomes whose corresponding value of X is less than or equal to a.
If is a vector-valued random variable, with values in, and thought of as a column vector, then the natural generalization of variance is, where and is the transpose of, and so is a row vector.
If is a complex-valued random variable, with values in, then its variance is, where is the conjugate transpose of.
If the attacker is spoofing source addresses randomly, the backscatter response packets from the victim will be sent back to random destinations.

If and experiment
If three dice are tossed, a trial is one toss of one die and the experiment is composed of three trials.
If the response variable is expected to follow a parametric family of probability distributions, then the statistician may specify ( in the protocol for the experiment or observational study ) that the responses be transformed to stabilize the variance.
If the experiment were done in English, since Searle knows English, he would be able to take questions and give answers without any algorithms for English questions, and he would be affectively aware of what was being said and the purposes it might serve: Searle passes the Turing test of answering the questions in both languages, but he's only conscious of what he's doing when he speaks English.
::" If anyone imagines that we are stating the case too strongly, let him try an experiment with the first bright boy he meets by asking,
If there are T treatments and T – 1 orthogonal contrasts, all the information that can be captured from the experiment is obtainable from the set of contrasts.
If morning rush traffic can be heard from outside, if researchers or maintenance staff appear at the same time each day, an experiment can be ruined by masking.
Since counter-clockwise may be defined in terms of up, forward, and right, this experiment unambiguously differentiates left from right using only natural elements: If they were reversed, or the atoms spun clockwise, the radiation would follow the spin axis instead of being opposite to it.
If the aether was dragged by mass then this experiment would have been able to detect the drag caused by the lead, but again the null result was found.
If at any time the subject indicated his desire to halt the experiment, he was given a succession of verbal prods by the experimenter, in this order:
If the subject still wished to stop after all four successive verbal prods, the experiment was halted.
If, in some future experiment, one of the mass-related phenomena is shown to not be proportional to the others, then that specific phenomenon will no longer be considered a part of the abstract concept of mass.
If one throws a die once, it is difficult to predict the outcome, but if we repeat this experiment many times, we will see that the number of times each result occurs divided by the number of throws will eventually stabilize towards a specific value.
If that happens, Franks said, “... the Western world, the free world, loses what it cherishes most, and that is freedom and liberty we ’ ve seen for a couple of hundred years in this grand experiment that we call democracy .” Franks then offered “ in a practical sense ” what he thinks would happen in the aftermath of such an attack.
If they are describing experiments or calculations, they must supply enough details that an independent researcher could repeat the experiment or calculation to verify the results.
In 2002, psychologist Richard Wiseman and colleagues at the University of Hertfordshire, UK, finished a year-long LaughLab experiment, concluding that of all animals, ducks attract the most humor and silliness ; he said, " If you're going to tell a joke involving an animal, make it a duck.
If outcomes of different runs of an experiment differ in any way that matters, they are distinct outcomes.
If Randall ’ s claim that the host may chase off possible dangers to the cleaner will be proved right, an experiment might be constructed in which reciprocity could be demonstrated.
If we modify this experiment so that one slit is closed, no interference pattern is observed.
If an experiment is carefully conducted, the results usually either support or disprove the hypothesis.
If the experiment is repeated with other colors, the color which has a majority will still rarely win.
If the experiment is repeated using approval voting, where voters are encouraged to vote for as many candidates as they approve of, then the winner is much more likely to be any one of the five marbles, because people who prefer green will be able to vote for every one of the green marbles.
If the subjects in the experiment are suspicious of the researcher, they are unlikely to behave as they normally would, and the researcher ’ s control of the experiment is then compromised ( p. 807 ).
In a 1975 retrospective article, Gold commented that his policy with If was to experiment, using new writers that had not yet established themselves.

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