Practice By Tag: Random Variables and Expectation

Question: 2022 Winter Final - 20

1 . 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)

$50^{-3}\cdot\sum_{i=1}^{50} i\cdot i^2$

(b)

$50^{-3}\cdot\sum_{i=1}^{50} i\cdot i^3$

(c)

$50^{-3}\cdot\sum_{i=1}^{50} i\cdot (3(i-1)^2 + 3(i-1) + 1)$

(d)

$33$

(e)

$99/2-49.5$