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This is not a homework question but something I thought of while reading.

In the method of maximum likelihood estimation, they're trying to maximize the likelihood function

[itex] f(\vec{x}| \theta ) [/itex] with respect to [itex]\theta[/itex]. But shouldn't the likelihood function be defined as [itex] f(\theta| \vec{x} ) [/itex] since we are GIVEN the data vector [itex] \vec{x} [/itex] while [itex] \theta [/itex] is the unknown parameter?

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# Why is likelihood function defined as such?

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