The random variable $W$ has the distribution $\mathrm{B}\left( n,p \right)$ and a mode $m$. By

Question

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

Accepted Answer

Shown: $m \geq E(W) + p - 1$

2022 NJC P2 Q5

2022 NJC P2 Q5

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