If x and y are real numbers, and if the graph of y is plotted against x, the derivative measures the slope of this graph at each point.

If Alice measures − x, the system collapses into state IIa, and Bob will get + x.

If he or she is also chief executive, he or she can thus politically control the necessary executive measures without which a proclaimed law can remain dead letter, sometimes for years or even forever.

If fleas or ticks are found, aggressive measures are in order.

# If A is a disjoint union of countably many disjoint Lebesgue measurable sets, then A is itself Lebesgue measurable and λ ( A ) is equal to the sum ( or infinite series ) of the measures of the involved measurable sets.

If the navigator measures the direction in real life, the angle can then be drawn on a nautical chart and the navigator will be on that line on the chart.

Alice could send bits to Bob in the following way: If Alice wishes to transmit a " 0 ", she measures the spin of her electron in the z direction, collapsing Bob's state to either or.

If comrade Molotov can manage to postpone the war for two or three months that will be our good fortune, but you yourselves must go off and take measures to raise the combat readiness of our forces ".

: If a person traveling with a yardstick, measures the length of such yardstick, the physical quantity of length would be written as

If each of two hypothetical experimenters, Alice and Bob, has one of the particles that form an entangled pair, and Alice measures the spin of her particle, the measurement will be entirely unpredictable, with a 50 % probability of the spin being up or down.

If Alice then " measures " her half-coin, by opening her envelope, for her the measurement will be unpredictable, with a 50 % probability of her half-coin being " heads " or " tails ", and Bob's " measurement " of his half-coin will always be opposite, hence perfectly anti-correlated.

If the latter occurs, ( Alice measures 1 ) then Bob's measurement will return 0 with certainty.

If one measures by arc length one finds that the shortest path connecting two points lying entirely in the sphere is a segment of the great circle containing the points ; see geodesic.

:: If Alice wishes to transmit a ' 0 ', she measures the spin of her electron in the z direction, collapsing Bob's state to either | z +>< sub > B </ sub > or | z ->< sub > B </ sub >.

If Alice wishes to transmit a ' 1 ', she measures the spin of her electron in the x direction, collapsing Bob's state to either | x +>< sub > B </ sub > or | x ->< sub > B </ sub >.

If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar.

If directional shear between the surface and the height in the atmosphere at which the barometric pressure measures is greater than 60 degrees, nothing more than flurries can be expected.

If the directional shear between the body of water and the vertical height at which the pressure measures is between 30 and 60 degrees, weak lake-effect bands are possible.

If the micrometer measures 0. 7503 ", then it is out of calibration.

If these measures are insufficient to make the blood temperature in the brain match the new setting in the hypothalamus, then shivering begins in order to use muscle movements to produce more heat.

If the union rate is $ 60 per page and 20 measures were orchestrated then the orchestrator's bill would be $ 300 plus 10 % for health and pension.

As an example, if one measures the position with an accuracy of, and the momentum with an accuracy of, then If we make further measurements in order to get more information, we disturb the system and change the trajectory into a new one depending on the measurement setup ; therefore, the measurement results are still subject to Heisenberg's uncertainty relation.

If elimination or substitution measures cannot be achieved, engineering controls and administrative controls, which seek to design safer mechanisms and coach safer human behavior, are implemented.

If they failed, the provincial government could carry out the necessary measures and charge the costs to the landowner or municipality.

If the function R is well-defined, its value must lie in the range, with 1 indicating perfect correlation and − 1 indicating perfect anti-correlation.

If the signal matches the desired user's code then the correlation function will be high and the system can extract that signal.

If the desired user's code has nothing in common with the signal the correlation should be as close to zero as possible ( thus eliminating the signal ); this is referred to as cross correlation.

If the code is correlated with the signal at any time offset other than zero, the correlation should be as close to zero as possible.

If the variables are independent, Pearson's correlation coefficient is 0, but the converse is not true because the correlation coefficient detects only linear dependencies between two variables.

If x and y are results of measurements that contain measurement error, the realistic limits on the correlation coefficient are not − 1 to + 1 but a smaller range.

If, as the one variable increases, the other decreases, the rank correlation coefficients will be negative.

If a population or data-set is characterized by more than two variables, a partial correlation coefficient measures the strength of dependence between a pair of variables that is not accounted for by the way in which they both change in response to variations in a selected subset of the other variables.

If r is the correlation observed for a particular trait, then:

If the 22 % correlation was an artifact partly based on factors such as rural recordkeeping, economic, class or ethnic differences in birth patterns, this fact would be blurred by this non-random selection.

If there are no repeated data values, a perfect Spearman correlation of + 1 or − 1 occurs when each of the variables is a perfect monotone function of the other.

If one considers the correlation function between random variables representing the same quantity measured at two different points then this is often referred to as an autocorrelation function being made up of autocorrelations.

If it is not, then more complicated correlation functions can be defined.

If the probability distribution has any target space symmetries, i. e. symmetries in the space of the stochastic variable ( also called internal symmetries ), then the correlation matrix will have induced symmetries.

If there are symmetries of the space ( or time ) in which the random variables exist ( also called spacetime symmetries ) then the correlation matrix will have special properties.

If there are symmetries, then the correlation function can be broken up into irreducible representations of the symmetries — both internal and spacetime.

Another possible reason is negative correlation between risk aversion ( e. g., the willingness to purchase insurance ) and risk level ( estimated ex ante based on observation of the ex post occurrence rate of observed claims ) in the population: If risk aversion is higher amongst lower risk customers, such that persons less likely to engage in risk-increasing behavior are more likely to engage in risk-decreasing behavior ( i. e., to take affirmative steps to reduce risk ), adverse selection can be reduced or even reversed, leading to ' propitious ' or ' advantageous ' selection.

If the theory is described by a path integral, a CPT transformation takes states to their conjugates, so that the correlation function

If we have two sets of variables, and, and there are correlations among the variables, then canonical correlation analysis will enable us to find linear combinations of the's and the's which have maximum correlation with each other.

If we have independent observations in a sample and is the estimated correlation for.