The Century dictionary and cyclopedia; a work of universal reference in all departments of knowledge, with a new atlas of the world .. . asi^uis isp,should occur just k times among these n occasions, isetiual to the term containing p* in the development of(p t-7)*, where ^ = 1 — p. Thus, suppose the event is theappearance of head when a coin is tossed up, so that p =q = I, and the coin be tossed up six times. Then the proli-ahilitics of 0,1, 2, 3, 4, 5, (i heads respectively are ,,,, ,;,,,u, iii, nii .o r,i- Tbc most probable value of k is thatwhole nuniber next less than (11 + t)p, unless thi
The Century dictionary and cyclopedia; a work of universal reference in all departments of knowledge, with a new atlas of the world .. . asi^uis isp,should occur just k times among these n occasions, isetiual to the term containing p* in the development of(p t-7)*, where ^ = 1 — p. Thus, suppose the event is theappearance of head when a coin is tossed up, so that p =q = I, and the coin be tossed up six times. Then the proli-ahilitics of 0,1, 2, 3, 4, 5, (i heads respectively are ,,,, ,;,,,u, iii, nii .o r,i- Tbc most probable value of k is thatwhole nuniber next less than (11 + t)p, unless this be itselfa whole nnmber, when it is equally pr<ibable. \Nhcn thenumber of trials is large, the probabilities of the ditfer-eiit numbers of ocenrrences of the given event are pro-Iiortional to areas included between the so-called proba-bility curve, its asymptote, and ordinatcs at successive dis-tances equal to 1/k2/ip7. This probability curve, whoseequation is ,1/ = o—lu —?»- (where 0 is the circnmferencefor unit diameter, and a is the Napierian base), is repre-sented in the figure, where the approximate straightness. Curvy. of the slope w ill be remarked. If it is desired toascortalnthe probability of the occurrence from k, to fr.^ times in-clusive in 11 ti-iuls of an event whose pnihable oceurrcneeat each trial is p, the approximate value is the area iiiclinl-cd between the probability curve, the asymptote, and thetwo ordinates, for which *•,-(« +Dp ^ *., + 1 - (n -h \)p probably Twice the quadratures of the areas arc given in treatiseson probabilities as tallies of the thela function of pi-olia-bililies. The chief practical application of probability isto ; and its only sigiiittcanee lies in an assur-ance as to the avcnige result in the long run. The theoryof probability is to be regarded as the logic of the physi-cal sciences. 3. Anylliing that has the appearance of realityor truth. Both the rocks and the earth arc eo splendent to beh
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Keywords: ., bookcentury1800, booksubjectatlases, booksubjectenglishlanguage
