2022 NJC P2 Q5
The random variable $W$ has the distribution $\text{B}\left( n,p \right)$ and a mode $m$. By considering the inequality $\text{P}\left( W=m \right)\ge \text{P}\left( W=m+1 \right)$, show that
$m\ge \text{E}\left( W \right)+p-1$
[3]
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