We take a sample of adults and measure their heights. If we record the gender of each person, we can calculate the average height and the variance of the height, separately, for men and women. Suppose, however, that this informa- tion was not recorded. Would it be possible to still obtain this information? Explain.
What will be an ideal response?
The height of men and women will have separate Gaussian distributions with
different means and perhaps different variances. By using a mixture model
approach, we can obtain estimates of the mean and variance of the two height
distributions. Given a large enough sample size, the estimated parameters
should be close to those that could be computed if we knew the gender of
each person.
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