14.2 Exercise 24

$E \left[\right. Y \left|\right. X = t \left]\right. = \frac{2}{3} \left(2 - t\right)$ and X has density function $f_{X} \left(t\right) = \frac{15}{16} t^{2} \left(2 - t\right)^{2} 0 \leq t < 2$. Determine $E \left[Y\right]$.