Class Size and Class Heterogeneity We study how class size and composition affect the academic and labor market performances of college students, two crucial policy questions given the secular increase in college enrollment. We rely on the random assignment of students to teaching classes. Our results suggest that a one standard deviation increase in the class-size would result in a 0.1 standar...

A computer model that incorporates the monochromatic aberrations of the eye is used to determine the optimal pupil size for axial and lateral resolution as it applies to retinal imaging instruments such as the confocal scanning laser ophthalmoscope. The optimal pupil size for axial resolution, based on the aberrations of 15 subjects, is 4.30 mm +/- 1.19 mm standard deviation (sd), which is larg...

The performance of the standard hierarchy of ab initio models--that is, Hartree-Fock theory, second-order Moller-Plesset theory, coupled-cluster singles-and-doubles theory, and coupled-cluster singles-doubles-approximate-triples theory--in combination with correlation-consistent basis sets is investigated for equilibrium geometries of molecules containing second-row elements. From an analysis o...

Definition 28.1.2 The variance of a random variable X with expectation μ = E[X] is the quantity V[X] = E [ (X − μ) ] = E [ X2 ] − μ2. The standard deviation of X is σX = √ V[X]. Theorem 28.1.3 (Chebychev inequality) Let X be a random variable with μx = E[X] and σx be the standard deviation of X. That is σX = E [ (X − μx) ] . Then, Pr [|X − μX | ≥ tσX] ≤ 1 t2 . This work is licensed under the Cr...

In the approach phase of the long jump, athletes attempt to strike the take-off board accurately with minimum loss of speed, and in an optimum body position for take-off. Previous research has shown that skilled long jumpers demonstrate an ascending-descending trend of variability rather than a consistent pattern of foot placement over trials. The present study examined whether non-long jumpers...