In the Previous Problem, the Eigenfunction Expansion If $x e ^ { t }$

question 14

Multiple Choice

In the previous problem, the eigenfunction expansion if $x e ^ { t }$ is

• A) \(e ^ { t } \sum _ { n - 1 } ^ { \infty } ( - 1 ) ^ { n } 2 L \cos ( n \pi x / L ) / ( n \pi )\)
• B) \(e ^ { t } \sum _ { n - 1 } ^ { \infty } ( - 1 ) ^ { n } 2 L \sin ( n \pi x / L ) / \left( n ^ { 2 } \pi ^ { 2 } \right)\)
• C) \(e ^ { t } \sum _ { n - 1 } ^ { \infty } ( - 1 ) ^ { n } 2 L \cos ( n \pi x / L ) / \left( n ^ { 2 } \pi ^ { 2 } \right)\)
• D) \(e ^ { t } \sum _ { n - 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } 2 L \cos ( n \pi x / L ) / ( n \pi )\)
• E) \(e ^ { t } \sum _ { n - 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } 2 L \sin ( n \pi x / L ) / ( n \pi )\)

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Definitions:

Population Means

The average value of a characteristic in a population.

90% Confidence

A statistical term indicating that there is a 90 percent chance that the true parameter is within the calculated confidence interval.

Standard Deviation

An statistical measure that quantifies the dispersion or spread of a set of data points around their mean value.

Sample Variances

The measure of dispersion within a sample set of data, indicating how much the values in the sample differ from the mean of the sample.