1 .
You choose a uniformly random element, say $a$, from the set $\{1,2,\dots,100\}$, and you choose a
uniformly random element, say $b$, from the same set $\{1,2,\dots,100\}$. ($a$ and $b$ are chosen
independently of each other.) Define the random variable $X$ to be
- X = $\max(a,b)$.
(a)
${\sum_{k=1}^{100}} k \cdot \frac{2k}{100^{2}}$
(b)
${\sum_{k=1}^{100}} k \cdot \left( \frac{1+2(k-1)}{100^{2}} \right)$
(c)
${\sum_{k=1}^{100}} k \cdot \frac{k^{2}}{100^{2}}$
(d)
${\sum_{k=1}^{100}} k \cdot \frac{k(k-1)}{100^{2}}$