Moment 2


Moment 2 :

(1) The product of a distance and another parameter. The moment may be about a point, line, or plane; if the parameter is a vector, the moment is the vector product of the vector distance from the point, line, or plane, into the parameter. Thus, the moment of the momentum of a fluid parcel per unit volume about an axis is r x pv, where r is the vector from axis to the parcel, p the density, and v the velocity vector of the parcel; this is Also called: the angular momentum. The moment of a force F about an axis is r x F, called the torque. The second moment of a parameter is the moment of the first moment; and so on, for higher moments. (2) By analogy, in statistical terminology, the mean value of a power of a random variable. The symbol P-B'(or v„) >s used f°r a raw moment as distinguished from the corresponding central moment p^'taken about the mean p. Thus the raw moments are: p„' =v„ = £(*"), („ = 0,1,2,...), where E(xf) is the expected value of the variant x to the nth power. In particular, p</ = 1 and nl' = The central moments are M„ = v„ = E[(x-/i)-], (n = 0,l,2,...), where E[(x: p)n] is the expected value of the nth power of the deviation of the variate from its mean. In particular, p„ = 1, p, = 0, Pj s a2< wnere a2 is the variance. N.B. Refer to source to verify equation(s) 

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