(Solved): An certain brand of upright freezer is available in three different rated capacities: \( 16 \mathr ...

An certain brand of upright freezer is available in three different rated capacities: \( 16 \mathrm{ft}^{3}, 18 \mathrm{ft}^{3} \), and \( 20 \mathrm{ft}^{3} \). Let \( X= \) the rated capacity of a freezer \( ^{2} \) this brand sold at a certain store. Suppose that \( X \) has the following \begin{tabular}{l|ccc} \( x \) & 16 & 18 & 20 \\ \hline\( p(x) \) & \( 0.3 \) & \( 0.4 \) & \( 0.3 \) \end{tabular} (a) Compute \( E(X), E\left(X^{2}\right) \), and \( V(X) \). \[ \begin{aligned} E(X) &=\\ E\left(X^{2}\right) &=\\ V(X) &= \end{aligned} \] (b) If the price of a freezer having capacity \( X \) is \( 62 X-650 \), what is the expected price paid by the next customer to buy a freezer? \$ (c) What is the variance of the price paid by the next customer? (d) Suppose that although the rated capacity of a freezer is \( X \), the actual capacity is \( h(X)=X-0.009 X^{2} \). What is the expected actual capacity of the freezer purchased by the next customer? (Enter your answer to four decimal places.) \[ \mathrm{ft}^{3} \]