For certain ore samples, the proportion Y of impurities per sample is a random variable with density function
$$f(y) = \begin{cases}
\frac{7}{2}y^6 + y, & 0 \le y \le 1, \\
0, & \text{elsewhere}.
\end{cases}$$
The dollar value of each sample is W = 7 - 0.7Y. Find the mean and variance of W. (Round your answers to four decimal places.)
E(W) =
V(W) =
Daily total solar radiation for a specified location in Florida in October has a probability density function given by
$$f(y) = \begin{cases}
\frac{3}{4}(y-4)(6-y), & 4 \le y \le 6, \\
0, & \text{elsewhere},
\end{cases}$$
with measurements in hundreds of calories. Find the expected daily solar radiation for October, in hundreds of calories.
E(Y) =
hundred calories