Use the Change of Variables $x = a u$ $y = b v$

question 69

Short Answer

Use the change of variables $x = a u$ , $y = b v$ , $z = c w$ to evaluate $\iiint _ { E } y d V$ , where E is the solid enclosed by the ellipsoid $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } + \frac { z ^ { 2 } } { c ^ { 2 } } = 1$ .

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Definitions:

Identical Populations

Populations in statistical studies that have exactly the same characteristics, distributions, and parameters.

Permutation Resamples

A statistical technique for obtaining null distributions by calculating all possible values of a test statistic under rearrangements of the observed data.

Null Hypothesis

A statement positing that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.

Bootstrap Resamples

Sampling method involving repeatedly drawing samples, with replacement, from a dataset to estimate the distribution of a statistic.