A question reads:
A loss random variable has a continuous uniform distribution on the interval $(0, 100)$.
A insurance policy on the loss pays the full amount of the loss if the loss is less than or equal to $40$. If the loss is above $40$ but less than or equal to $80$, then the insurance pays $40$ plus one-half of the loss in excess of $40$. If the loss is above $80$, the insurance pays $60$. If $Y$ denotes the amount paid by the insurance when a loss occurs, find the variance of $Y$. http://www.sambroverman.com/pqw/aug20-07p.pdf
The solution uses the formula for variance based on the Expected value. It calculates the expected value of $Y$ as:
$$E[Y] = \int_0^{40} x(.01)dx + \int_{40}^{80} (20 + .5x)(.01)dx + \int_{80}^{100} (60)(.01)dx $$
Why do we multiple the function in each integral by $.01$?