The average value of any function, f(x), between x= a and x= b is
Here, a= 0 while b is "infinity"- there is no upper bound.
So the average is a limit-
I'm not sure if this is the right forum, but it's from the course on DE...
I'm stuck on understanding the first part of a question:
"In a large population, the proportion with income between x and x+dx is f(x)dx. Express the mean (average) income *mu* as an integral, assumiing that any positive income is possible."
Can someone point me in the right starting direction?
For anyone else who is interested, I asked my supervisor for help, so here's the answer;
If the population has N people, the number with income in the range x to x+dx is Nf(x)dx
We multiply this by x to get the sum of their incomes.
So the total income is
Hence the mean income,
Not simply the integral of f(x), which is perhaps why HallsofIvy's post is a little unclear.