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Multiple Scenarios: Parametric and Non-Parametric Data
NP
Since we do not need to assume that data of gene disorders and certain diseases is drawn from populations with any parametrized distributions.
5.
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Relativity: Differential Geometry
147380 Relativity: Differential Geometry A particle moves along a parametrized curve given by
x(lamda)=cos(lamda), y(lamda)=sin(lamda), z(lamda)=lamda
Express the path of the curve in the spherical polar coordinates {r, theta, pheta}
where x =
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Integral
(a) the curve is parametrized by x = -1 + 2t and y = 0, with 0 =< t =< 1, in which case dx = 2 dt and dy = 0; hence the integral becomes
int_{0, 1} (0 + 1) (2 dt) = 2
(b) in this case x = cos (t) and y = sin (t) with t running from
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parametric and nonparametric hypothesis test
The term non-parametric statistic can also refer to a statistic (a function on a sample) whose interpretation does not depend on the population fitting any parametrized distributions.
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Orthogonality, Orthonormal Basis and Orthogonal Complement
You will get a parametrized vector - as expected since there are infinite numbers of vectors that are orthogonal to the initial two: if C is orthogonal to them, so is rC where r is a real number.
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Computing the Mass of a Thin Shell
Solution: We have
M = ∫S δ(x, y) dA = ∫S(1 + x2 + y2) dA,
where S is the surface of the shell, which is parametrized by x and y, i.e.
S = {(x, y): x2 + y2 ≤ 4}.
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Multivariable Calculus: Surfaces Given Parametrically
(Give equations in x, y, and z for the surfaces in parametrized by X and Y
For X(S, t), take x = s cost, y = s sint, and z = 3s2
Then, x2 + y2 = s2(cos2t + sin2t) = s2 = z/3
Therefore, z = 3x2 + 3y2
When s = 0 and t = 0, x = 0 and y = 0.
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Curves in euclidean 3-space
Consider the following curves that pass through p:
Curve 1: xi (λ) = (λ, (λ-1)2, - λ)
Curve 2: xi (μ) = (cos μ , sin μ, μ-1)
Curve 3: xi (σ) = (σ2, σ3 + σ2, σ)
The curves are parametrized by the parameters that vary, at least in
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Pricing and demand estimates
Retail demand is parametrized as semilog and doublelog with diffuse priors for the models and the parameters. Wholesale demand functions are derived by incorporating the retailers' pricing behavior in the retail demand function.