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The difference between μ and x¯ is μ is a population parameter, x¯ is a sample parameter Both are the mean, hence they are equal μ is observed, x¯ is conceptual x¯ is estimated, μ is observed
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\[\mu\ is\ a\ population\ parameter,\ \bar {x}\ is\ a\ sample\ parameter\]
so where you have doubt.whatever you have written is right.
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