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Hou, Juncheng; Nadarajah, Saralees – International Journal of Mathematical Education in Science and Technology, 2019
It is well known that two events A and B are independent if and only if . Here, we derive a condition for independence not well known. We then extend the condition for independence of n events.
Descriptors: Probability, Mathematical Concepts, Mathematics Education
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Nadarajah, Saralees; Chu, Jeffrey; Chan, Stephen – International Journal of Mathematical Education in Science and Technology, 2019
A correlation coefficient taking positive values is introduced. It is more easily understood than other correlation measures especially in social science contexts. Estimation issues are addressed. A data application is given.
Descriptors: Correlation, Mathematics Instruction, Computation, Statistical Analysis
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Withers, Christopher S.; Nadarajah, Saralees – International Journal of Mathematical Education in Science and Technology, 2012
For n = 1, 2, ... , we give a solution (x[subscript 1], ... , x[subscript n], N) to the Diophantine integer equation [image omitted]. Our solution has N of the form n!, in contrast to other solutions in the literature that are extensions of Euler's solution for N, a sum of squares. More generally, for given n and given integer weights m[subscript…
Descriptors: Statistical Analysis, Geometric Concepts, Numbers, Equations (Mathematics)
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Withers, Christopher S.; Nadarajah, Saralees – International Journal of Mathematical Education in Science and Technology, 2012
We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…
Descriptors: Mathematics Instruction, Equations (Mathematics), Validity, Mathematical Logic
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Withers, Christopher S.; Nadarajah, Saralees – International Journal of Mathematical Education in Science and Technology, 2011
The linear regression model is one of the most popular models in statistics. It is also one of the simplest models in statistics. It has received applications in almost every area of science, engineering and medicine. In this article, the authors show that adding a predictor to a linear model increases the variance of the estimated regression…
Descriptors: Regression (Statistics), Computation, Models, Prediction
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Withers, Christopher S.; Nadarajah, Saralees – International Journal of Mathematical Education in Science and Technology, 2010
We extend the well-known identity, log det A = tr log A, for any square non-singular matrix A.
Descriptors: Algebra, Matrices, Equations (Mathematics)
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Withers, Christopher S.; Nadarajah, Saralees – International Journal of Mathematical Education in Science and Technology, 2009
Moments and cumulants are expressed in terms of each other using Bell polynomials. Inbuilt routines for the latter make these expressions amenable to use by algebraic manipulation programs. One of the four formulas given is an explicit version of Kendall's use of Faa di Bruno's chain rule to express cumulants in terms of moments.
Descriptors: Algebra, Mathematical Formulas, Statistics, Probability