Suppose there is some population consisting of $100$ individuals where $98$ of the individuals are $25$ years old and $2$ individuals are $20$ years old.
The following facts can be shown to be true about a sample of size two that is to be collected from this population:
The probability that the sample will have two 25-year-olds is $.9602$
The probability that the sample will have one 25-year-old and one 20-year-old is $.0396$
The probability that the sample will have two 20-year-olds is $.0002$
Let $X$ be the mean age of the sample. Find the variance of $X$.