The regression curve of daily quantity demanded of tablet computers in a Midwestern market, measured in thousands of units and expressed as a function of price, all else held equal, is given by

\(\mathrm{E}(\mathrm{Q} \mid p)=10 p^{-.5}\)

The marginal probability density function of price is given by

\(f(p)=\frac{3}{8} p^{2} I_{[0,2]}(p)\)

(a) Derive the value of quantity demanded, \(\mathrm{E}(\mathrm{Q})\).

(b) Derive the expected value of dollar sales, \(\mathrm{E}(P Q)\).