We typically have multiple data observations which we use to estimate a paramete

Question

We typically have multiple data observations which we use to estimate a parameter of interest. (In class, we used the example of estimating the height of the average student at a college. We would collect a random sample of students and measure their heights, and then use the sample mean as an estimation of the population mean.) We nearly always assume that our observations are drawn ‘iid’—independent and identically distributed. Why is the assumption that the observations are independent mathematically convenient? (Hint: Think about the product term in the likelihood function, and how this simplifies conditional probabilities if the observations are independent.)

Explanation / Answer

The way the likelihood function is calculated is by assuming the elements in the sample are all independent identiacally following the same probabilty distributions, thus makes us easy by just aplyin p(X=xi) and multiplying because we have independent condition

This makes the likelihood function to look simpler and also we can easily calculate the maximum likelihood estimator.

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