Question: Average age in a population. Suppose the 100 -vector \(x\) represents the distribution of ages in some population of people, with \(x_{i}\) being the number of \(i-1\) year olds, for \(i=1, \ldots, 100\). (You can assume that \(x \neq 0\), and that there is no one in the population over age $99 .$ Find expressions, using vector notation, for the following quantities.

1. The total number of people in the population.
2. The total number of people in the population age 65 and over.
3. The average age of the population. (You can use ordinary division of numbers in

your expression.)

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