Question: 2022 Winter Final - 20
Let $X_1,X_2,X_3$ be three numbers chosen independently and uniformly from the set $\{1,\ldots,50\}$. Let $Z=\max\{X_1,X_3,X_4\}$. What is $ E(Z) $?
(a)
$50^{-3}\cdot\sum_{i=1}^{50} i\cdot i^3$
(b)
$99/2-49.5$
(c)
$50^{-3}\cdot\sum_{i=1}^{50} i\cdot i^2$
(d)
$50^{-3}\cdot\sum_{i=1}^{50} i\cdot (3(i-1)^2 + 3(i-1) + 1)$
(e)
$33$