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Thus and variable
Thus we do not score the number of bull's-eyes, and the random variable is not the number of successes.
Thus, variable only depends directly on variable, rather than depending on the entire set of variables.
Thus, the variable named ' Car ' can have subscripts " Door ", " Steering Wheel " and " Engine ", each of which can contain a value and have subscripts of their own.
Thus in determining whether to shut down a firm should compare total revenue to total variable costs ( VC ) rather than total costs ( FC + VC ).
Thus a is considered to be a parameter: it is less variable than the variable x or y, but it is not an explicit constant like the exponent 2.
Thus the variance is a measure of the amount of variation of the values of that variable, taking account of all possible values and their probabilities or weightings ( not just the extremes which give the range ).
Thus it was suggested that Vega showed occasional low-amplitude pulsations associated with a Delta Scuti variable.
Thus the concept of a random function is one example of a random element and hence is a generalization of the simpler idea of a random variable.
Thus a polynomial in one variable x can be written as
Thus according to the central limit theorem, we can model jitter as a gaussian random variable.
Thus an algorithm to find isolated real roots of a low-degree polynomial in one variable may bear little resemblance to an algorithm for complex roots of a " black-box " function which is not even known to be differentiable.
Thus, the German Historical School focused on specific dynamic institutions as the largest variable in changes in political economy.
Thus, a dummy variable can be defined as a qualitative representative variable incorporated into a regression, such that it assumes the value 1 whenever the category it represents occurs, and 0 otherwise.
Thus, if more than 1 qualitative variable is included in the regression, it is important to note that the omitted category should be chosen as the benchmark category and all comparisons will be made in relation to that category.
Thus, an interaction dummy ( product of two dummies ) can alter the dependent variable from the value that it gets when the two dummies are considered individually.
Thus there are many sorts of quantifiers, two for each sort of variable.
Thus I ( X ; X ) ≥ I ( X ; Y ), and one can formulate the basic principle that a variable contains at least as much information about itself as any other variable can provide.
Thus the two-dimensional Fourier transform of the initial function is the one variable Fourier transform of the Radon transform of that function.
Thus in an image processing context the original image ƒ can be recovered from the ' sinogram ' data Rƒ by applying a ramp filter ( in the variable ) and then back-projecting.
Thus, research into alien Overtechnology culminated in the development of the variable fighters for the U. N. Spacy.

Thus and which
Thus we are compelled to face the urbanization of the South -- an urbanization which, despite its dramatic and overwhelming effects upon the Southern culture, has been utterly ignored by the bulk of Southern writers.
Thus with regard to the loss of tradition, in the change from order to disorder the metaphysics of change works itself out as a disruption of the individual soul, a change in which man continues as an objective ontological existent, but no longer as a man.
Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.
Thus Trevelyan repeats the story which pictured Victor Emmanuel as refusing to abandon the famous Statuto at the insistence of General Radetzky.
Thus science is the savior of mankind, and in this respect Childhood's End only blueprints in greater detail the vision of the future which, though not always so directly stated, has nevertheless been present in the minds of most science-fiction writers.
Thus the government simultaneously undertook the vast burden of social security which had traditionally been privately discharged, and created a national scarcity which has engendered calamitous problems of social security.
Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.
Thus, there has come into being a situation in which the state must raise all of its own revenues and, in addition, must give assistance to its local governments.
Thus, in the last few years, a number of programs which looked very promising at the time their development was commenced have since been completely eliminated.
Thus was invented the single thread sewing machine, which Mr. Gibbs in partnership with Mr. Willcox decided to bring to Brown & Sharpe with the proposal that the small company undertake its manufacture.
Thus, direct comparisons can be drawn with free burning arcs which have been studied in detail during the past years and decades by numerous investigators ( Ref. 3 ).
Thus the Af are projections which correspond to some direct-sum decomposition of the space V.
Thus Af is also continuous at Af, and in a neighborhood of Af which does not contain a tangent point.
Thus in a context in which there has been discussion of snow but mention of local conditions is new, dominant stress will probably be on here in it rarely snows here, but in a context in which there has been discussion of local weather but no mention of snow, dominant stress will probably be on snows.
Thus in Mary wrote an account of the trip first strong stress on Mary marks Mary as the first in a series of people who wrote accounts of the trip, strong stress on wrote marks the writing as the first of a series of actions of Mary's concerned with an account of her trip ( about which she may later have made speeches, for example ), and strong stress on trip makes the trip the first of a series of subjects about which Mary wrote accounts.
Thus, besides the training provided to youth in school, the existence of the school program can have supplementary benefits to industry which make it an asset to industrial development efforts.
Thus far, the cases which have come before the courts have involved only the issue of referral where the job is vacant due to a strike -- condition ( 1 ) in the Regulation of the Secretary.
Thus, when specifically permitted, the operand of a given line on the Autocoder coding sheet may be continued in the operand of from one to four additional lines which immediately follow.
Thus, when Dartmouth's Winter Carnival -- widely recognized as the greatest, wildest, roaringest college weekend anywhere, any time -- was broadcast over a national television hookup, Prexy John Sloan Dickey appeared on the screen in rugged winter garb, topped off by a tam-o'-shanter which he confessed had been acquired from a Smith girl.
Thus some provinces contained tribes which detested each other, and to them independence meant an opportunity for war.
Thus the image of God is that which makes a man a man and not an oyster ; ;
Thus, a well-planned adobe wall of the appropriate thickness is very effective at controlling inside temperature through the wide daily fluctuations typical of desert climates, a factor which has contributed to its longevity as a building material.

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