In the Previous Three Problems, the Solution For $u ( t )$

question 20

Multiple Choice

In the previous three problems, the solution for $u ( t )$ is

• A) \(u _ { n } ( t ) = ( - 1 ) ^ { n } 2 L \left( e ^ { t } - e ^ { - n ^ { 2 } a ^ { 2 } t / L ^ { 2 } } \right) / ( n \pi ( 1 + n \pi / L ) )\)
• B) \(u _ { x } ( t ) = ( - 1 ) ^ { n } 2 L \left( e ^ { t } + e ^ { - n ^ { 2 } x ^ { 2 } t / L ^ { 2 } } \right) / \left( n \pi \left( 1 + n ^ { 2 } \pi ^ { 2 } / L ^ { 2 } \right) \right)\)
• C) \(u _ { x } ( t ) = ( - 1 ) ^ { n + 1 } 2 L \left( e ^ { t } + e ^ { - n ^ { 2 } x ^ { 2 } t / L ^ { 2 } } \right) / \left( n \pi \left( 1 + n ^ { 2 } \pi ^ { 2 } / L ^ { 2 } \right) \right)\)
• D) \(u _ { x } ( t ) = ( - 1 ) ^ { n + 1 } 2 L \left( e ^ { t } - e ^ { - n ^ { 2 } x ^ { 2 } t / L ^ { 2 } } \right) / \left( n \pi \left( 1 + n ^ { 2 } \pi ^ { 2 } / L ^ { 2 } \right) \right)\)
• E) \(u _ { n } ( t ) = 2 L \left( e ^ { t } - e ^ { - n ^ { 2 } x ^ { 2 } t / L ^ { 2 } } \right) / \left( n \pi \left( 1 + n ^ { 2 } \pi ^ { 2 } / L ^ { 2 } \right) \right)\)

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Definitions:

Unbiased Estimators

Statistical estimators whose expected value is equal to the parameter being estimated.

Variance

A measure of the dispersion indicating how much the values in a data set differ from the mean.

Relatively Efficient

Describes a statistical estimator or procedure that has lower variance or better performance compared to others under certain conditions.

Point Estimate

A single value given as an estimate of a population parameter, often derived from sample data.