Alex and his friend stand randomly in a queue with $3$ other people. The random variable $X$ is the

Question

Alex and his friend stand randomly in a queue with $3$ other people. The random variable $X$ is the number of people standing between Alex and his friend. Show that $\mathrm{P}\left( X=2 \right)=0.2$. [2] Tabulate the probability distribution of $X$. [2] Find $\mathrm{E}\left( X \right)$ and $\mathrm{E}{{\left( X-1 \right)}^{2}}$. Hence find $\mathrm{Var}\left( X \right)$. [3]

Accepted Answer

$\mathrm{E}(X)=1$, $\mathrm{Var}(X)=1$

2017 ACJC P2 Q6

2017 ACJC P2 Q6

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