Measuring the position of an oscillating massNo. ofoccurrencesMeasuredvaluespringn1x1n2x2n3x3+Forceconstantk(N/m)....x=0nmxmx 0xfinalWhat is the average value of x?U(x)E11;iiNNiiiin xn xxNnK.E.1iNiiNn0xo‐xo2
When we do not have a predictable outcome for a measurement, we must dealwith probability densities and/or probability distributionsConsider someThe probability distributionwith probability densities and/or probability distributions. Consider somequantity that varies continuously, for example the height of a Purdue student.Wecould coerce a group of students to report their height and we couldmake a plot of height in 10-cm intervals as shown below. Nobody will be exactly180 cm or 190 cm tall, so we just group students into height intervals andsystematically round things up at the edges of each bin.If we wantfiner detail, we could group heights in 1-cm intervals or 1-mmintervals, which will continue to make things discrete.But as the intervalsbllthhi tbltiThii3become smaller, the histogram resemblesa continuous curve. This curve isknown as theprobability distribution.http://theochemlab.asu.edu/teaching/phy571/supp02.pdf
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